2022-07-20: What If We Live in a Superdeterministic Universe?
- 17:34: The second law of thermodynamics says that entropy must increase in the forward time direction.
2022-06-15: Can Wormholes Solve The Black Hole Information Paradox?
- 00:26: ... resolve it have led to stunning realizations about the nature of entropy, quantum information, and even to the holographic principle. ...
- 02:24: ... way to think about this paradox is in terms of entropy. Think of entropy as the amount of information hidden ...
- 02:43: ... quantum version of entropy is called von Neumann entropy. This is the entropy of ...
- 03:20: ... radiation a permanent and unrecoverable non-zero von Neumann entropy. ...
- 04:21: ... Von Neuman entropy of the radiation should increase over time as the internal ...
- 05:20: ... information leaks out this way, then the von Neumann entropy of Hawking radiation should rise over time as more and ...
- 06:01: ... versa. Physicists have managed to explore black hole entropy using these holographic methods, and even managed to produce the ...
- 08:36: ... to get a proper calculation of the von Neuman entropy of Hawking radiation, you need to consider all transitional states ...
- 10:06: ... computing the von Neumann entropy, there is a neat mathematical trick you can do. For some ...
- 10:42: ... Renyi entropy is found using the gravitational path integral. For a spacetime ...
- 11:13: ... black hole, you end up with a new equation for the entropy of the Hawking ...
- 11:25: ... a bunch of its clones is enough to leave an imprint on the entropy. This results in a new equation for the entropy of the ...
- 12:09: ... the island rule, the physicists found that the von Neumann entropy of Hawking radiation exactly follows the Page curve. ...
2022-06-01: What If Physics IS NOT Describing Reality?
- 09:26: ... This approach uses the informational definition of entropy - Shannon entropy - which is a measure of the number of ...
2022-02-10: The Nature of Space and Time AMA
- 00:03: ... there's a metric to determine the flow time that that is other than entropy okay so by that uh they mean a way of defining the arrow time the ...
2022-01-12: How To Simulate The Universe With DFT
- 18:04: Energy becomes useful when it’s moved between a low entropy to a high entropy configuration.
- 18:10: ... releasing exactly as much energy as it absorbed, but in a much higher entropy ...
- 18:43: Such a beam has a lower entropy than isotropic thermal radiation, and so less energy is made available for the aliens.
2021-11-17: Are Black Holes Actually Fuzzballs?
- 01:48: Black holes should have an enormous number of so-called microstates - hidden configurations - and this translates to an enormous entropy.
- 01:58: ... formula for black hole entropy was discovered by Jakob Bekenstein, who, incidentally, also inspired the ...
- 02:37: So the air has the very high entropy of lots of information that is hidden under very few macroscopic properties.
- 03:04: The information contributing to black hole entropy could be beneath the horizon, but if we add one more fact we run into serious trouble.
- 06:49: And the number they found exactly agreed with the Bekenstein formula for black hole entropy.
- 07:04: The infinitesimal strings and branes of string theory might be the analog of the molecules that store the entropy of our room full of air.
- 07:40: ... model to see if it could reproduce properties of black holes beyond the entropy. ...
2021-11-10: What If Our Understanding of Gravity Is Wrong?
- 07:43: ... the Bekenstein bound, which connects black hole information content to entropy, as well as other black-hole-related ...
2021-11-02: Is ACTION The Most Fundamental Property in Physics?
- 00:02: ... obscure concept in physics that may be more fundamental than energy and entropy and perhaps time itself. Ready? Action. In order to wrench the laws of ...
2021-07-07: Electrons DO NOT Spin
- 13:49: ... we talked about the connection between quantum entanglement and entropy - this was a heady topic to say the least, but you guys had such ...
- 13:59: ... Paul Duffey asks whether entropy is an illusion created by our observation of isolated components ...
- 14:32: ... Neumann entropy is different to thermodynamic entropy in that it represents the ...
- 15:09: ... asks the following: If entropy only increased over time, which implies it was at its minimum at the Big ...
- 15:31: ... and it was also extremely smooth. The compact part is where the low entropy comes from. The “gravitational degrees of freedom” were almost ...
- 16:27: ... - but that’s not necessarily the case. Remember that von Neumann entropy is relative to the system you’re talking about, and so is ...
- 17:20: In other words, the universe - or our patch of it - may have started out unentangled and at low entropy, even if it was at thermal equilibrium.
2021-06-23: How Quantum Entanglement Creates Entropy
- 00:00: ... Entropy is surely one of the most perplexing concepts in physics. It’s ...
- 00:27: ... great astrophysicist Arthur Eddington once said, “The law that entropy always increases holds, I think, the supreme position ...
- 01:02: ... it’s not obvious what makes it so fundamental. A system’s entropy is what we call an emergent property, and the 2nd law seems to ...
- 01:45: ... than the properties and laws governing individual particles. Entropy IS a thermodynamic property, and the 2nd law is the … well, ...
- 02:13: ... getting quantum - and there is indeed a type of entropy that applies to quantum systems like our air molecule - it’s von ...
- 02:34: ... we dive into that, let’s review the more familiar definitions of entropy. To really understand these we have a full playlist on the ...
- 02:48: ... Clausius came up with the first definition of entropy as essentially the amount of useful work that could be ...
- 03:45: ... theory to really see the connection between information and entropy. It was Claude Shannon who founded the field of Information ...
- 04:19: ... way to think about Shannon entropy is in terms of events. The more possible outcomes, the ...
- 04:50: ... origin story goes, he only started calling his invention “entropy” after talking to the great Hungarian mathematician and physicist ...
- 05:19: ... von Neumann probably knew perfectly well that Shannon’s entropy was the real deal. One because von Neumann was a savant ...
- 05:55: ... concept of von Neumann entropy is at least incredibly powerful. It’s at the heart of quantum ...
- 06:38: ... To get a glimmer of understanding of what von Neumann entropy is about, let’s think about information in quantum ...
- 07:44: ... then there is no hidden information - which means its entropy - its von Neumann entropy - is zero. Observing the coin ...
- 08:42: ... it just isn’t known to you. So the regular coin's entropy - in this case its Shannon entropy - is ...
- 09:22: ... means 50% heads tails and 50% tails heads. The von Neumann entropy of that entire wavefunction is still zero because the ...
- 10:15: ... we can connect von Neumann entropy to all of the other forms of entropy, and glimpse the real origin of the second ...
- 10:23: ... tails. And, just like the regular, classical coin - it has non-zero entropy. ...
- 12:26: ... un-quantum macroscopic world, but it also drives the growth of entropy. ...
- 13:09: ... time which itself points in the direction of increasing entropy and multiplying entanglement, as, of course, we’ve discussed. But ...
2021-05-25: What If (Tiny) Black Holes Are Everywhere?
- 09:14: ... perfect thermal spectrum then, by definition, that radiation has maximum entropy and contains no information about whatever fell into the black ...
2021-03-23: Zeno's Paradox & The Quantum Zeno Effect
- 13:04: ... you’ll explore everything from time in quantum mechanics to black hole entropy and learn what cutting-edge science has to say about the nature of ...
2020-12-15: The Supernova At The End of Time
- 00:21: ... short is that the universe ends in heat death, as it approaches maximum entropy, and its eternal exponential expansion drives it to effective utter ...
2020-12-08: Why Do You Remember The Past But Not The Future?
- 00:39: The 2nd law of thermodynamics dictates that entropy must rise over time.
- 00:48: As long as we have a single timestamp in a highly ordered state, there’ll be a gradient of increasing entropy on either side of it.
- 01:43: ... understand why memories are formed in the same direction as increasing entropy. ...
- 09:14: ... laws of physics. It's just insanely unlikely. As unlikely as decreasing entropy. ...
- 09:25: So the key to understanding how our brains inherit the arrow of time lies in understanding the connection between entropy and correlation.
- 09:35: Another way to define increasing entropy is as increasing correlation between elements in a system.
- 09:41: ... by sharing energy - which is another way to think about the rise in entropy. ...
- 09:54: ... universe started in a state of extremely low entropy - spatially separated regions were definitely uncorrelated with each ...
- 10:06: Over time, connections and correlations were made as entropy grew.
- 10:10: So you have a direction in which correlations tend to increase - the same direction as entropy.
- 10:17: ... Entropy is increasing universe-wide, but the smallest chunks of the universe - ...
- 10:29: ... physics prefers one time direction over the other - it’s just that a low entropy allows correlations and memories - to build in one direction and not the ...
- 11:09: Just as our bodies expend entropy by using and redistributing energy.
- 11:14: ... talk about this properly we’d really want to talk about how entropy is also connected to the spreading of quantum entanglement. If you have ...
- 11:34: ... one way the arrows of time plays out, tracing the gradient of increasing entropy and correlation and memory away from the inexplicably low entropy ...
- 11:52: ... we explored how our universe gains its directionality to time from entropy and the 2nd law of thermodynamics - or as Ryan Gallagher always hears it ...
- 12:10: ... universe were reversed - time ran backwards to the big bang, wouldn’t entropy appear to increase as all structure disassembled and formed the ...
- 12:23: ... does appear to have been random - which we normally associate with high entropy. ...
- 12:34: How, then, was it low entropy?
- 12:38: The answer is that the low entropy came from how compact the universe was compared to how spread out it could be.
- 12:58: ... Penrose puts it this way - in the early universe the low entropy was not in the degrees of freedom of the matter - that stuff was high ...
- 13:18: Ryan Christopherson asks whether the random nature of quantum mechanics isn’t a larger hurdle to the reversibility of time than entropy.
2020-11-18: The Arrow of Time and How to Reverse It
- 00:54: ... reassemble. Our whole universe decays in the inexorable rise in entropy as time ticks forward. The other place we perceive the arrow of time is ...
- 01:21: ... we’re going to dive into the first part of this - How does entropy break the symmetry of time, and cause the future to differ from the ...
- 03:12: ... to this. The second law of thermodynamics states that this stuff called entropy must always increase or stay constant - entropy never decreases over ...
- 04:13: ... randomly spread out, then over time it’ll become more spread out. Entropy measures how randomly distributed the energy in a system is. Higher ...
- 04:50: ... just tells us how a system is likely to change from a position of low entropy - in either time direction. To understand why one particular direction ...
- 05:10: ... start with a handful of particles with low entropy. You can do low entropy by having a weird distribution of velocities, but ...
- 06:00: ... low-entropy system and look at steps either before or after it in time, entropy is likely to be higher. Entropy actually doesn’t care about the ...
- 06:19: ... point, you perceive an asymmetry in time - particles expanding, entropy increasing on one side, or particles converging,and entropy decreasing ...
- 06:52: The real-world situation represented by this diagram is called an entropy fluctuation.
- 06:57: ... experience entropy decrease very occasionally and, typically, on very small scales due to ...
- 07:17: ... it’s no accident I chose “expanding particles” to illustrate evolving entropy. When we measure the velocities of particles across our universe - in the ...
- 08:11: ... extreme density of the Big Bang and its corresponding ridiculously low entropy? This is actually an open question in physics, and we’re not going to ...
- 09:25: ... is true - but if it was true we’re presented with a fun scenario. If entropy increases backwards in time before the big bang, does that mean time ...
- 09:39: ... the thermodynamic arrow of time - the flow of time defined by increasing entropy -connected to our sense of the flow of time? Why do we experience time ...
2020-10-13: Do the Past and Future Exist?
- 03:36: ... of cause and effect, evolving patterns of structure and information, entropy, and even our conscious experience, which itself emerges in the forward ...
2020-09-21: Could Life Evolve Inside Stars?
- 08:12: If energy is concentrated in certain places we would call that an ordered, low entropy situation.
- 08:56: Little low-entropy blips like life ultimately accelerate the increase in entropy of the universe.
2020-06-30: Dissolving an Event Horizon
- 15:36: ... your car’s expiring warranty” “Smedjip was here" "Hey folks, Enjoy your entropy while it's low." And a gratifying number of Hitchhikers Guide to the ...
2020-06-15: What Happens After the Universe Ends?
- 11:35: In particular, to explain its extremely low entropy.
- 11:39: If entropy can only rise over time, per the second law of thermodynamics, how did it get so low at the start?
- 11:56: But Penrose insists that this does not explain the low entropy of the big bang.
- 12:01: ... Bang singularity helped Penrose to demonstrate that the smallness of the entropy at the Big Bang is due to the tiny entropy in the gravitational field at ...
- 12:40: For the daisy-chain-verse to give you low entropy big bangs, you need to actually clean the entropy slate between aeons.
- 12:48: To do that, black holes must swallow entropy - and destroy information.
2020-03-31: What’s On The Other Side Of A Black Hole?
- 14:15: ... seems analogous to the second law of thermodynamics - aka that entropy must increase over ...
- 14:25: ... observation - but it's not just analogous - entropy and entanglement seem to be fundamentally connected. I've been meaning ...
2020-03-16: How Do Quantum States Manifest In The Classical World?
- 16:29: ... possible combination of quantum events exists and if the increase of entropy is probabilistic, then is it inevitable that there are exceptionally ...
2020-02-24: How Decoherence Splits The Quantum Multiverse
- 13:55: There’s a lot more to discuss - including the connection to quantum entanglement and to entropy.
2020-02-03: Are there Infinite Versions of You?
- 09:14: ... Bekenstein and Steven Hawking showed that the maximum amount of entropy in any region of space is proportional to the number of tiny Planck ...
2019-12-09: The Doomsday Argument
- 11:05: ... you could be a momentary entropy fluctuation that caused a brain with exactly your current mental ...
2019-11-18: Can You Observe a Typical Universe?
- 05:33: The universe’s most finely-tuned parameter is its unthinkably low initial entropy.
- 05:50: ... to the evolution of life - has been powered by the slow increase in entropy from that initial ...
- 06:01: ... of its perhaps-infinite life in a state of extreme disorder and high entropy - iron stars, black holes, and a mist of cold elementary particles, not ...
- 06:16: ... second law of thermodynamics tells us that entropy can only increase, which means extreme high entropy states must be the ...
- 08:15: This refined anthropic principle gets really interesting when applied to our low entropy big bang.
- 08:21: ... low-entropy regions happened just by chance fluctuations from a high entropy state, then the lower the entropy the less probability of that region ...
- 08:48: ... a life-bearing planet - so there should be many more observers in small entropy fluctuations than in large ...
- 09:23: Apparently we aren’t, and so we can probably rule out a simple random entropy fluctuation as a sufficient explanation for our big bang.
2019-10-15: Loop Quantum Gravity Explained
- 11:20: ... example, the theory seems to predict Hawking radiation and black hole entropy consistent with Hawking and Bekenstein’s ...
2019-07-15: The Quantum Internet
- 01:37: ... the concept of information and certain fundamentals of physics - such as entropy, and also quantum ...
2019-04-10: The Holographic Universe Explained
- 01:19: The story started with black holes, and with Jacob Bekenstein, who derived an equation to describe their entropy.
- 01:27: A black hole’s entropy represents the amount of quantum information of everything that ever fell into it.
- 01:34: This Bekenstein bound represents maximum possible entropy-slash-information of any volume of space.
2019-03-13: Will You Travel to Space?
- 15:47: You'll always lose energy as entropy increases. And you can never not have some entropy.
- 16:00: ... Like by stealing their aces aka energy, and giving them your 2's aka entropy, and Yeah, this is where we leave particle gambling metaphors to the ...
2019-03-06: The Impossibility of Perpetual Motion Machines
- 00:43: ... break the second law of thermodynamics - extracting energy by reversing entropy. ...
- 03:07: ... review: the 2nd law states that entropy can never decrease over time – in other words, energy will tend to ...
- 03:26: Machines of the second kind claim to be able to tap reservoirs of energy that are already evenly spread – effectively reversing the growth of entropy.
- 04:30: This is actually a specific example of a Maxwell’s demon device, an entropy-reversing thought experiment that we’ve discussed before.
2019-01-16: Our Antimatter, Mirrored, Time-Reversed Universe
- 10:54: ... in the asymmetry between matter and antimatter then there's the whole entropy business although it's connection to quantum mechanics is still not well ...
2018-10-18: What are the Strings in String Theory?
- 14:59: But most of the information in the universe is in black holes, or more accurately, most entropy or hidden information is in black holes.
2018-10-10: Computing a Universe Simulation
- 03:16: ... the maximum possible amount of hidden information, the maximum possible entropy. ...
- 09:53: ... estimate the computational history of the universe by assuming that all entropy generated over the history of the universe comes from its internal ...
- 10:02: The Landauer limit gives the entropy cost for computation.
- 10:06: And approximating very crudely, it's 1 bit of entropy per operation.
- 10:12: Matter and radiation combined have an entropy of 10 to the power of 90 bits.
2018-09-20: Quantum Gravity and the Hardest Problem in Physics
- 13:12: Today, we're covering both the black hole entropy enigma and the challenge question episode.
2018-09-12: How Much Information is in the Universe?
- 01:30: ... principle episode is still coming, but our recent episode on black hole entropy and some of the lead-ups to that might be helpful ...
- 01:57: Jacob Bekenstein figured this out by realizing that the entropy of a black hole is proportional to the surface area of its event horizon.
- 02:05: ... entropy is just a measure of hidden information, so the Bekenstein bound is ...
- 06:34: So almost all of the information, and for that matter, the entropy in particles is in neutrinos and in the cosmic microwave background photons.
- 07:02: As I mentioned last time, black holes contain most of the entropy in the universe.
- 07:06: The relationship between black hole entropy and information deserves some thought.
- 07:10: ... hole entropy in terms of number of bits tells you the information you'd need to ...
- 07:22: 2 to the power of the number of bits of entropy.
- 07:25: And for black holes, that entropy is the Bekenstein bound, the number of Planck areas on its event horizon.
- 08:04: So the Milky Way's black hole has as much entropy and hidden information as all of the matter and radiation in the entire rest of the universe.
- 08:20: We're talking something like 10 to the power of 101 to 10 to the power of 102 bits of entropy or information.
- 08:26: Black holes contain, by far, most of the entropy in the universe, and require most information to fully describe.
- 09:56: Let's ignore really high entropy stuff like black holes, the cosmic background radiation, and neutrinos.
- 11:30: ... episodes today, and next week, we'll get to responses to black hole entropy, as well as today's ...
2018-09-05: The Black Hole Entropy Enigma
- 00:07: Black holes seem like they should have no entropy, but in fact they hold most of the entropy in the universe.
- 00:15: [MUSIC PLAYING] At first it seemed that black holes were so simple they should have no entropy.
- 00:25: Well, it turns out they contain most of the entropy in the universe.
- 01:15: But they also present an apparent conflict with the notion of entropy and the second law of thermodynamics.
- 01:42: But first, you are going to need to know more about why black holes contain most of the universe's entropy.
- 03:09: It all began with Jacob Bekenstein thinking about black-hole entropy.
- 03:14: OK, first, entropy.
- 03:26: Go and watch that background stuff if you're behind, but of course for now I'll give you a quick TLDW on entropy.
- 03:33: So we can think of entropy in two ways.
- 03:38: High entropy means thermal equilibrium.
- 03:46: ... two, entropy measures the amount of unknown information that you would need to ...
- 03:55: The higher the entropy, the more randomly distributed its particles and the more possible configurations lead to the same macroscopic state.
- 04:03: ... higher the entropy, the less you can guess about the properties of individual particles ...
- 04:12: ... so the second law of thermodynamics states that entropy of an isolated system must always increase, which means energy tends to ...
- 04:29: Let's make a black hole and see what happens to entropy.
- 04:36: Now that's a high entropy based, super hot and full of randomly moving particles.
- 05:07: ... of space in which the black hole formed appears to have gone from high entropy to zero entropy in an instant, shattering the second law in the process, ...
- 05:24: If quantum information is stored on the surface of the black hole, can't we store entropy there also?
- 05:30: And then why not radiate the entropy back into the universe as Hawking radiation?
- 07:02: Bekenstein saw a close correspondence between the always-increasing event-horizon surface area and the always-increasing nature of entropy.
- 07:10: ... in its mass closely resembles the original definition of thermodynamic entropy. ...
- 07:21: Just replace change in entropy and internal thermal energy with change in black-hole surface area and black-hole mass, respectively.
- 07:38: Bekenstein had just discovered black-hole thermodynamics, but that didn't give him the exact definition for black-hole entropy.
- 07:45: For that, he turned to Ludwig Boltzmann's informational definition for entropy.
- 07:50: So entropy can be defined as the information hidden in a system's macroscopic configuration times the Boltzmann constant.
- 08:37: ... that information content by the Boltzmann constant and you have the entropy of a black hole, which is going to be directly proportional to the ...
- 08:48: Bekenstein's connection between surface area and entropy could have been a coincidence, at least until Stephen Hawking came along.
- 09:13: So if black holes have a temperature, then they also have entropy.
- 09:18: Good old-fashioned thermodynamic entropy tells us that change in entropy is change in internal thermal energy divided by temperature.
- 09:26: ... along with black-hole mass for internal energy and figured out the total entropy contained in a black ...
- 09:42: ... you get the same result for black-hole entropy whether you figure it out from the amount of information that gets ...
- 10:01: The second law of thermodynamics is saved because black holes do have entropy.
- 10:06: In fact, they have enormous entropies, the maximum possible, so much that black holes are now believed to contain most of the entropy in the universe.
2018-08-23: How Will the Universe End?
- 01:05: In fact, our universe will spend almost all of its infinite time in darkness, slowly crawling towards maximum entropy and ultimate heat death.
- 01:19: ... many ways for the universe to cool down, dissipate energy, and gain entropy. ...
- 01:51: ... to figure out how long before the universe reaches its final maximum entropy, minimum interesting state, and answer the questions, how long before ...
- 11:54: ... approaches heat death in which all energy is perfectly distributed, entropy has peaked, and there's nothing for any future civilization to cling to, ...
2018-08-01: How Close To The Sun Can Humanity Get?
- 10:04: Thereby, decreasing entropy against the second law of thermodynamics.
- 11:45: And if energy is coming in from the outside, then it's OK for entropy to decrease.
2018-07-25: Reversing Entropy with Maxwell's Demon
- 00:15: Entropy is sometimes described as a measure of disorder or randomness.
- 00:19: The second law of thermodynamics, the law that entropy must on average increase, has been interpreted as the inevitability of the decay of structure.
- 00:31: As we saw in our episode on the physics of life, structure can develop in one region even as the entropy of the universe rises.
- 00:38: Ultimately, entropy is a measure of the availability of free energy, of energy that isn't hopelessly mixed into thermal equilibrium.
- 00:50: But entropy is connected to disorder and randomness in a very real way.
- 00:55: See, entropy is a measure of ignorance.
- 00:58: Entropy very directly measures how much information we don't have about a system.
- 01:27: There, we show that entropy is a direct measure of hidden information.
- 02:15: These all correspond to the same smoothly distributed macrostate and to maximum entropy.
- 03:04: This is close to minimum entropy.
- 03:35: Again there's only one arrangement like this, so it should also be low entropy right?
- 03:51: In fact, this configuration isn't low entropy in the thermodynamic sense.
- 03:59: Thermodynamic entropy is related to the amount of hidden information, based on thermodynamic knowledge only.
- 04:17: Thermodynamic entropy is low if there are differences in the average thermodynamic properties from one macroscopic region compared to another.
- 04:26: ... are just weird microstates among the many microstates of a very high entropy ...
- 04:39: So much for structure and organization always meaning low entropy, right?
- 04:43: ... actually, it turns out that even these specific high entropy configurations can be transformed to low entropy, as long as we have ...
- 05:06: ... that entropy was a statistical phenomenon, he came up with a thought experiment to ...
- 05:30: The halves are in thermal equilibrium with each other, and if the box is isolated from its surroundings, then this is the state of maximum entropy.
- 06:08: We are no longer in thermal equilibrium, and the entropy is lower than before the demon started.
- 06:20: But all of this appears to have been done without exchanging energy or entropy with the outside universe.
- 06:26: ... seems to violate the second law of thermodynamics, which demands entropy remain constant or increase, unless energy is exchanged with the outside ...
- 06:46: ... and open the door, mechanisms which, in principle, don't increase entropy. ...
- 06:58: But it turns out, there's one last step in the process of sorting particles where the increase of entropy is unavoidable.
- 07:58: That's a physical process that reduces the demon's internal entropy, and that takes an irreversible transfer of energy.
- 08:07: The demon has to radiate heat, which means transferring entropy back into the box or to the universe.
- 08:23: ... merging of two computation paths, must be accompanied by a corresponding entropy increase." And this has come to be seen as a fundamental limit to the ...
- 08:42: Both Maxwell's conundrum and Landauer's resolution are fascinating, because they highlight the fundamental link between entropy and information.
- 09:16: But ultimately, possessing that information does increase entropy.
- 09:26: ... entropy of the universe must increase, and yet knowing the microstate of a ...
- 09:42: Claude Shannon, the father of information theory, was deeply inspired by the close connection between entropy and information.
- 09:49: He defined a new type of entropy, Shannon entropy.
- 10:11: So for example, the roll of a die has more entropy than the flip of a coin.
- 10:23: Shannon use the term entropy for this measure, because his formula was almost identical to the formula for thermodynamic entropy.
- 10:45: In fact, Shannon's entropy is, in a sense, just a generalization of thermodynamic entropy.
- 11:00: And there's a third, perhaps even more fundamental, type of entropy.
- 11:04: That's quantum entropy, also known as Von Neumann entropy.
- 11:17: ... the evolution of quantum entanglement may be the ultimate source of entropy, the second law, the limits of information processing, and even the arrow ...
- 11:30: ... episode of "Space Time." Last time, we delved into the true nature of entropy and the cause of the second law of ...
- 12:01: Starting with this assumption gets you to the Boltzmann equation, and it's a nice, relatively simple way to understand entropy.
- 12:13: If different microstates can have different probabilities, then you need to include those probabilities in your equation for entropy.
- 12:20: ... resulting formula, the Gibbs entropy equation, was derived soon after Boltzmann's equation, and is the more ...
- 12:31: Nifelheim Mists notes that if entropy is statistical, then it's wrong to say that it must always increase.
- 12:44: ... the likelihood of entropy decreasing for any macroscopic isolated system is so overwhelmingly ...
- 12:55: On the other hand, if the universe lasts for infinite time, then principal entropy drops of all sizes should eventually happen.
2018-07-18: The Misunderstood Nature of Entropy
- 00:07: ... Entropy and the second law of thermodynamics have been credited with defying the ...
- 00:23: But what is entropy really, and how fundamental is it to our universe?
- 00:28: [MUSIC PLAYING] Entropy is surely one of the most intriguing and misunderstood concepts in all of physics.
- 00:38: The entropy of the universe must always increase, so says the second law of thermodynamics.
- 01:13: ... nothing for it but to collapse in deepest humiliation." We've looked at entropy in the past, but it's time to go much deeper to unravel the great ...
- 01:24: ... upcoming episodes, we'll explore different aspects and consequences of entropy, including its role in black hole thermodynamics and how it will lead to ...
- 01:34: But today, we'll see what entropy really is and why the second law of thermodynamics is considered to be so fundamental and so unavoidable.
- 02:28: Around a half century after Carnot, Rudolf Clausius was inspired to quantify this tendency of heat energies to decay over time, enter entropy.
- 02:37: Clausius defined entropy as the internal property that changes as heat energy moves around within a system.
- 02:44: Specifically, the change in entropy of each reservoir is the heat energy going into or out of that reservoir divided by its temperature.
- 02:53: For a Carnot cycle, the overall change in entropy is zero but for any less efficient cycle, entropy increases.
- 03:01: In fact, an increase in entropy means that the heat reservoirs are approaching the same temperature, reducing the capacity to do useful work.
- 03:10: Carnot and Clausius' work revealed entropy as a measure of how evenly spread out a system's energy is.
- 03:17: ... the best you can hope for is that the separation of energy and the entropy remain ...
- 03:35: ... understanding of entropy is in terms of flowing heat, and it came from the days when many, ...
- 03:46: ... took a revolution to understand the reality of entropy, that revolution was statistical mechanics, founded by the great Ludwig ...
- 07:38: Statistical mechanics tells us why large-scale systems have the properties they do, but what does this have to do with entropy?
- 07:47: ... Boltzmann equation tells us that entropy is the logarithm of the number of microstates consistent with the ...
- 07:57: So our smoothly spread out equilibrium Go board has a high entropy and our clustered board has low entropy.
- 08:21: Order is not the same thing as low entropy, and the second law isn't always the tendency towards disorder.
- 08:27: ... thermodynamic entropy, the only special arrangements of particles that change entropy are the ...
- 08:40: ... get deeper into that, we'll need to talk about information entropy, which we'll also need for black hole thermodynamics and will take ...
- 08:49: So the macrostate that defines thermodynamic equilibrium is, by definition, the one with the most microstates, which also means the maximum entropy.
- 08:59: ... system not in equilibrium must increase in entropy, simply because at any future time, it's current microstate will most ...
- 09:24: In both cases, you are reducing the number of accessible microstates which, by definition, must reduce entropy.
- 09:34: Heat must flow between your system and the outside universe in a way that increases the entropy of the universe as a whole.
- 09:41: ... mechanics inevitably leads to entropy and the second law, and it does so by something so fundamental and basic ...
- 09:56: The inevitability of the rise of entropy is as fundamental as counting, that's why Einstein and Eddington were so sure of it.
- 10:04: But entropy is also statistical and emerges from behavior of particles under the laws of motion.
- 10:33: We talked a little about this in our episode on the physics of life, where we saw how entropy drives both the increase and decay of complexity.
- 10:40: It's almost like the concept of time is emergent and statistical, just like entropy.
- 11:29: Check it out, because we'll be doing more stat mech and delving deeper into entropy in the future.
2018-06-20: The Black Hole Information Paradox
- 11:22: ... has led to radical new ideas about the nature of information and entropy, exploded the field of string theory, and hinted at the possible ...
2018-05-02: The Star at the End of Time
- 01:15: For life to stave off rising entropy and decay, energy must flow.
2018-04-18: Using Stars to See Gravitational Waves
- 10:57: Bose-Einstein asks, is life causing the universe to reach high entropy faster than if life didn't exist?
- 11:36: But you decrease entropy locally.
- 11:42: Slimthrall suggests a flaw in the idea that life is a mechanism for increasing entropy.
- 12:20: Sometimes the conditions for a given path to low energy or to high entropy are unusual.
- 12:38: Well, thanks for joining us, Captain Entropy.
2018-04-11: The Physics of Life (ft. It's Okay to be Smart & PBS Eons!)
- 00:49: To understand life, we need to understand entropy.
- 01:18: Such a random disordered, unspecial arrangement is a high entropy state.
- 01:24: ... universe being crunched into an infinitely dense point are low entropy. ...
- 01:40: So entropy is sort of a measure of the boringness of a system, the commonness of the arrangement of particles.
- 01:48: The second law of thermodynamics tells us that a closed system will only increase in entropy.
- 01:57: But there's one type of system that seems to resist the second law of thermodynamics and maintain low entropy.
- 02:06: Life has a very low internal entropy because its structure is extremely specific and non-random.
- 03:20: ... in order appears to contradict the second law of thermodynamics-- entropy appears to either stay constant or ...
- 03:39: The second law tells us that closed systems must increase in entropy.
- 04:08: On the other hand, the system of the Earth plus the sun is increasing in entropy.
- 04:13: Life acts to reduce its own internal entropy by increasing the entropy of its surroundings.
- 04:19: ... pointed out by Ludwig Boltzmann, who described life as a struggle for entropy, well, more accurately, against entropy or for negative ...
- 04:29: Erwin Schrodinger, in his 1944 book, "What is Life," describes life as a process feeding on negative entropy.
- 07:57: Living things are incredible heat dissipation entropy-maximizing machines.
- 08:01: The most random possible form for energy is thermal radiation, and the lower the energy of its component photons, the higher the entropy.
- 08:10: A plant absorbs the concentrated ultraviolet light from the sun and reprocesses it into a much higher entropy infrared heat glow.
- 09:15: ... laminar flow has a lower entropy than the turbulent flow because there are fewer ways to rearrange the ...
- 09:39: ... given eddy taken separately has a lower internal entropy than its chaotic surroundings, but the source of that local incidence of ...
- 09:49: And those turbulent eddies ultimately serve to increase the entropy of the greater flow.
- 09:55: So given a much larger source of order, the global process of dissipation of that order results in eddies of low entropy.
- 10:06: In the case of life, the original source of extreme low entropy is the Big Bang itself.
- 10:20: These blips in order are actually serving the second law helping the universe disperse its early extreme low entropy state.
- 10:28: ... disorder and dullness, an agent in the inexorable trend to maximize the entropy of ...
2017-11-08: Zero-Point Energy Demystified
- 02:13: Well, the answer lies in entropy and the second law of thermodynamics.
- 02:18: Entropy can be thought of as a measure of the specialness of the arrangement of a system of particles.
- 02:24: Higher entropy means a more disordered arrangement.
- 02:34: The entropy of a closed system always increases.
- 03:40: Energy is extracted in the movement towards equilibrium in the increase of entropy.
2017-10-19: The Nature of Nothing
- 14:57: Temperature can be defined as the rate of change of thermal energy divided by the rate of change of entropy.
- 15:04: In normal, positive-temperature substances, entropy always increases as you add heat.
- 15:11: But when you stack particles towards the highest energy states, that's a special arrangement, making it low entropy.
- 15:20: Add more energy, and more particles reach the highest energy state, which decreases entropy further.
- 15:26: Entropy goes down as heat is added.
- 15:29: So if temperature is change in thermal energy over entropy, then temperature is negative.
2017-08-30: White Holes
- 09:05: Well, theoretically, yes, but to make one you would need to reverse entropy.
- 09:24: It demands that entropy, a measure of disorder, always increase.
- 09:35: You need to decrease entropy.
- 09:38: Now, this is technically possible because entropy is a statistical phenomenon.
- 09:43: Very rare reductions in entropy do happen.
- 09:46: ... long as globally entropy increases on average, it's conceivable that an incredibly rare entropy ...
- 09:58: However, it would immediately explode in a burst of energy as soon as entropy and time resumed their normal flow upwards and forwards.
- 10:09: We actually did talk about a case where a random drop in entropy lead to something very much like a white hole in this episode.
- 10:18: ... that the Big Bang itself came from such a profoundly improbable entropy dip, and as it happens, the Big Bang looks-- mathematically, at least-- ...
2017-05-03: Are We Living in an Ancestor Simulation? ft. Neil deGrasse Tyson
- 15:49: The pressure is as much a statistical emergent phenomenon as entropy.
2017-04-26: Are You a Boltzmann Brain?
- 00:53: Take entropy, for example.
- 00:55: Prior to Boltzmann, entropy was only understood as a measure of the proportion of energy in a system that can be used for useful work.
- 01:42: Entropy is a measure of how far from equilibrium a system is.
- 01:46: The lower the entropy, the further from equilibrium.
- 01:57: Entropy must always increase in a closed system.
- 02:00: And it's that flow back to equilibrium, that increase in entropy, that can be harnessed to do work.
- 02:10: Why does entropy always increase?
- 02:14: Entropy is just a measure of the specialness, or the degree of order, in the current arrangement of positions and velocities of a system's particles.
- 03:18: Entropy increases because particle positions and velocities get randomized over time.
- 03:23: Boltzmann's interpretation of entropy leads to a prediction that seems innocuous but has some astounding implications.
- 03:31: His statistical interpretation doesn't prohibit entropy from decreasing.
- 03:37: For example, tiny, localized dips in entropy happen all the time, when you get a chance convergence of a few particles in one corner of the room.
- 03:45: The larger the random dip in entropy, the less probable it is.
- 04:23: All sorts of dips in entropy will happen.
- 05:08: But, however it happened, entropy was extremely low at the instant of the Big Bang, and it's been increasing ever since.
- 05:16: ... "useful work" performed by that increase in entropy includes the formation of galaxies, stars, planets, Alan Tudyk-- indeed, ...
- 05:27: In the far future, the universe will reach maximum entropy.
- 07:05: So, aren't there more probable, smaller dips in entropy that could lead to conscious observers?
- 07:45: ... a universe where structure results from entropy fluctuations, the vast majority of conscious experiences that ever occur ...
- 08:00: It sounds ridiculous, but it's the logical conclusion if we assume a Big Bang from entropy fluctuations.
2016-04-06: We Are Star Stuff
- 04:40: As well as providing us with all of their glorious entropy-resisting energy, stars are element factories, stellar alchemists.
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