Foundations of the Second Law of Thermodynamics

Lecture description:

Nine people give short arguments about 2nd law:



Seth Lloyd discusses the Maxwell demon paradox and the spin-echo effect, and how in some cases, in an apparent violation of the Second Law of Thermodynamics “entropy goes up and whoa, goes down then up.” He notes that when the laws of thermodynamics appear not to be true, “we simply revise our opinions and re-describe” them, which is “a pathetic situation.”



Owen Maroney invokes “straightforward statistical mechanical assumptions” in his discussion of whether “something can violate the Second Law or not,” and raises Szilard’s engine and Landauer’s erasure principle.



Silviu Guiasu aims to show there is no contradiction between microscopic reversibility of classical mechanics, as described by Hamilton’s equations of motion, and macroscopic irreversibility as described by the increase of entropy.



Ping Ao believes the dynamics behind Darwinian evolution “provide a natural framework” for thermodynamics, and it remains to translate “global statements to precise mathematical language.”



Jochen Gemmer discusses bubbles in Hilbert space, while examining how we might overcome the apparent contradiction between quantum dynamics and thermodynamics.



Bernard Guy focuses on the link between the Second Law and the problem of time, seeking clues for understanding the opposition of reversibility and irreversibility. He sees clashing constructs of time and space in the separate worlds of cognitivists and physicists.



Gian Paulo Berretta praises the seminal work and “pioneering intuition” of Keenan and Hatsopoulos, which inspires new answers to such fundamental issues as whether entropy is an intrinsic property of matter, and if irreversibility is an intrinsic feature of microscopic dynamics.



Speranta Gheorghiu-Svirschevski believes a nonlinear approach can help reconcile the Second Law and quantum evolution. In particular, she looks for ways to “reconcile locality and separability,” while acknowledging that general wisdom says it’s not exactly possible.



Dorion Sagan says that “ever since Darwin, life has been considered an exception to the Second Law.” On the contrary, “entropy, rather, energy spread, and evolution are inextricably linked.” Sagan suggests that “life may just be another energy spreading system,” and “death is the name we give the inevitable disruption of a specific part of life’s network.”

Frontiers of the Second Law

Lecture description:

These nine panelists describe ways in which the Second Law of Thermodynamics can be stretched, or applied in less traditional ways. Adrian Bejan has constructed a law that “covers every configuration in physics, from animate, to inanimate, to us, the societal." Bejan demonstrates how his law describes and predicts the tree-shaped flow of all rivers, animal locomotion and human settlement distribution. With it, says Bejan, “thermodynamics becomes a science of systems with configuration…”



Bjarne Andresen acknowledges “many fights about the Second Law,” before declaring his belief that “entropy survives as a concept, and applies equally in the chemistry lab, to the quantum computer and to black holes.” He discusses the importance of carefully defining the system under examination beforehand, “otherwise you get into fights with your neighbors."



Miguel Rubi discusses how to use the Second Law to extract information about the evolution of small systems. Unlike “canonical thermodynamics,” which describe systems in terms of energy, volume and mass, mesoscopic thermodynamics focuses on systems in terms of positions and movement of particles. Some examples of processes explicable by this kind of thermodynamics include the translocation of ions, RNA unfolding under tension, and muscular contractions.



Signe Kjelstrup argues that mesoscopic nonequilibrium thermodynamics (MNET) can address a longstanding problem in classical nonequilibrium thermodynamics, by addressing “activated processes.” Biological systems have heat flow, says Kjelstrup, and “that is as of yet not included in the description of enzyme kinetics. It should be there to quantify lost work in these important systems.”



“An important question arising in nonequilibrium thermodynamics is not just entropy but temperature,” says David Jou, in particular, “the physical meaning of temperature.” Jou invokes the extended thermodynamics of viscoelastic systems, and looks for a simple model valid for a modest range of equations.



Miroslav Grmela suggests that any time one goes from details to some kind of pattern, “there is an entropy involved…by providing some kind of dissipation, some pattern recognition process.” Grmela believes that thermodynamics … “find a natural formulation in the setting of contact geometry.”



Lyndsay Gordon’s talk involves Maxwellian valves. He discusses “a machine based on an osmophoretic engine,” a simple system with a liquid membrane, solvent and solute, “that is fluctuating completely forever,” without information. “This thing goes by itself,” he says.



Eric Schneider discerns “laws of ecology” in such gradient systems as the energy flow between the sun and earth. “We can determine “…heat and entropy production in the system,” as well as “ecological successions and directional processes that directly tie them to Darwinian evolution.” He advises his colleagues “to encourage policy makers to use exergy analyses on future energy development projects.”



Symposium organizer George Hatsopoulos wraps up by noting “that as far as I know in thermodynamics, there is no statement that says the Second Law implies the increase of entropy. The Second Law only says that the entropy cannot decrease, but there’s nothing wrong with entropy staying put.” We have evidence that in some cases it appears the entropy increases, but that’s not the “Second Law.”

The Second Law and Statistical Mechanics

Lecture description:

Lecture is given by Dick Bedeaux. He patiently traces the evolution of the second law of thermodynamics from its formulation in the mid-19th century through today, from the perspective of statistical mechanics.



In its earliest form, as laid out by Rudolf Clausius, the law states that the entropy of the world always increases. This proposition in some sense launched the field of thermodynamics, according to Bedeaux: “It got going in order to understand exactly where the laws came from.” There was particular interest in exploring entropy in terms of the motions of particles. Scientists began refining theories around the behavior of gas in equilibrium, looking at density, velocity distribution, potential energy and heat conductivity. After Maxwell and Boltzmann appeared to have succeeded at a proof of the second law, other scientists questioned its validity: If Newton’s equations are reversible, they reasoned, why can’t a system in some sense reverse velocities and return along the same path? Others worked out the recurrence paradox, that “if you take any kind of motion in phase space and follow trajectories, that trajectory after a sufficiently long time will come arbitrarily close to the original point…” These two paradoxes posed a fundamental challenge to proofs of the second law.



The debate continued through the end of the 19th century, into the 20th, with additional efforts to refine the notion of entropy using concepts of probability -- courtesy of the burgeoning discipline of statistical mechanics, according to Bedeaux. This field enabled better descriptions of equilibrium and non-equilibrium states. There was “a lot of progress,” says Bedeaux: Einstein explained Brownian motion in 1905, and closer to our own era, scientists “punched a hole in the argument about the recurrence paradox,” using probabilistic descriptions. Nevertheless, in our own times, “in non-equilibrium statistical mechanics, there is as yet no fully satisfactory derivation of the second law.” To meet this challenge, a proof should provide a simple mechanical example, “like hard discs between reflecting walls, in order to be convincing.” While equations of motion on the microscopic level incorporating the idea of irreversibility demonstrate entropy production, it’s uncertain “whether Mother Nature believes this herself -- we must do experiments to verify,” concludes Bedeaux.

The Second Law and Quantum Physics

Lecture description:

In this often droll lecture on a very abstract subject, Charles Bennett explores entropy, “one of my long loves,” and how it relates to quantum information. He first reminds his audience that such information is reducible to qubits, a two-state system that can exist in a superposition of states -- such as the polarized photon. Bennett believes that “quantum mechanics helps resolves the paradox or puzzle of the origin of the second law” of thermodynamics—the irreversible increase of entropy. Classical science might invoke chaos dynamics or environmental effects to explain entropy. The quantum way of viewing it involves entanglement.



In classical mechanics, when two subsystems in a definite state interact “by some deterministic reversible interaction,” there will be a definite output for each subsystem. “The entropy of the whole thing will be 0+0=0.” But while the entropy output of two quantum systems interacting might be 0, the individual subsystems manage to have “as much entropy as they could possibly have.” This is due to entanglement, “a state of the whole system that cannot be described by attributing states to its parts. Two entangled photons can be said to be in a definite state of sameness even though neither has a polarization of its own.” Bennett acknowledges “this is an idea that’s hard to explain to many people,” although he believes that back in 1967, during the Summer of Love, many people “could understand this from an intuitive sense, if not mathematically.”



Bennett plays with the famous evanescence of quantum information, noting that the photons illuminating him fill up the room with “optical replicas of the shape of my nose.” But where do they go? He says, “If no record is made of which path a photon follows through an interferometer, or if a record is made but then unmade, the photons will have followed a superposition of both paths. Putting it in slightly theological terms, after the experiment is over, even God doesn’t remember which path it followed.”



Most classical information, such as “a pattern of snowflakes or grains of rice in last night’s dinner,” is impermanent, though occasionally frozen by a fossil-like process, Bennett says. It’s like a medallion he saw in a flea market: “In 1832, on this spot, nothing happened.” But even if information in our physical world is doomed to vanish, in spite of our digital-age efforts to duplicate everything, “the particular physics of our universe” viewed from the perspective of quantum dynamics, seems to “evolve in a complexity-increasing manner, under appropriate conditions,” concludes Bennett.

The Second Law and Cosmology

Lecture description:

In spite of its old age, the Second Law of Thermodynamics “is alive and kicking,” says Max Tegmark, stimulating research on “really, really big puzzles.” In Tegmark’s case, “big” encompasses the cosmos, and investigating the entropy of the universe offers one path into understanding “how we started out.”



Tegmark frames his talk with paradoxical questions: Why is entropy so low, and why is entropy so high? The first question is “crucial to understanding the arrow of time,” and involves the microscopic definition of entropy. 13.7 billion years after the Big Bang, entropy in the observable universe is in “the ballpark of 1089 bits -- crudely speaking, a google.” This is much lower than the theoretical limit to how much entropy our cosmos could contain. Also, Tegmark wonders, why has our solar system ended up so far from thermal equilibrium, since when the universe was younger, the temperature was almost the same everywhere?



It turns out that in cosmology, unlike classical physics, atoms start out at uniform density and end up, abetted by gravity, “clumpy,” with gas getting denser and forming stars. Tegmark shows a supercomputer simulation of this process, which depicts the evolution of a universe with galaxies and solar systems like our own. Different temperatures in the universe aren’t due to magic, he says, just Einstein’s theory of gravity and basic gas physics.



But, Tegmark ponders, why was the universe uniform in the beginning? One “crazy sounding answer” involves inflation. A tiny region of space much smaller than an atom, which is very uniform and very dense, begins to expand exponentially, until it makes up all space in our known universe. It gets weirder. Tegmark invokes inflation to explain not only the low entropy of the cosmos, but its high entropy as well. That same 1089 bits can also be viewed as “such a big number that it suggests…that we’re in some kind of multiverse, or some much larger reality than what we can observe.” The initial conditions that make up these 10 to the 89th bits “just tell us where in space we live, our address in space.” We should call the Big Bang “not the beginning but the end of inflation in this part of space. … If we zoom out in the universe, we should expect to see much more entropy.” If you don’t get this intuitively, that’s OK, Tegmark reassures us, but “if we categorically reject ideas in science just because they feel crazy, we will probably reject whatever the correct theory is, too.”

The Second Law and Biophysics

Lecture description:

“Biology is messy,” says Kenneth Dill, and it’s “heavily about entropy.” Just look at how biological systems repeat entropy at every possible turn: a parent cell making two daughter cells, sending one DNA molecule to each; and the process of biochemical reactions, with water getting stripped off the molecules. Dill is convinced that the “language of biology in the future will be nonequilibrium statistical mechanics.” He’s engaged in experiments that explore how dynamical laws apply to very small biological systems, such as those inside cells.



Traditional macro-scale dynamics, explains Dill, have laws where concentration gradients or temperature gradients drive flux. But inside cells, there are elements that sometimes contain five molecules, and then in the next instant, 500 molecules. The question is how to think about these highly fluctuating quantities in terms of dynamics. To that end, researchers have been devising experiments to describe the dynamics of micro systems.



Dill’s colleagues have built a microfluidics apparatus that plots the diffusion of microscopic particles over time, their probable routes and rates. To help frame this work, and make predictions about comparable systems, they use an analogy to entropy, described as caliber. Just as there can be maximum entropy, there can be maximum caliber -- “an extremum principle that predicts the dynamical laws, just as maximum entropy predicts equilibrium,” says Dill. This way of modeling fluxes deals with the likely trajectories and speeds traveled by particles within a certain time period.



Dill also describes how statistical mechanics applies in the “dog-flea model.” Scientists calculate the probabilities of fleas jumping from one dog to another, and of going up against a concentration gradient. Dill says this model can be used “to argue in the simplest way how diffusion works,” to predict flux distribution.



Scientists have also worked out an experiment to model two-state kinetic processes, such as single ion channels opening and closing. Colloidal particles wiggling in adjacent laser traps can jump over barriers from one trap to the other, depending on the height of the barrier and the depth of the well. This allows researchers to count trajectories, and to measure “the full dynamical distribution functions.” The value of the maximum caliber approach, Dill says, is that you get data about the first moment of the system in state “and from them you can predict everything else.” Says Dill, “One of the great things about having an extremum principle and partition-based approach is it turns out all kinds of analogies with normal thermodynamics.” So far, researchers have only taken the earliest steps to illustrate this new tack. “The potential power of caliber hasn’t been tested yet,” believes Dill.

The Second Law and Energy

Lecture description:

This Nobel Prize-winning scientist admits to staying up late the night before his talk to bone up on thermodynamics. He puts his research to good use, discussing the history and application of the laws of thermodynamics, which have served as “the scientific foundation of how we harness energy, and the basis of the industrial revolution, the wealth of nations.”



Taking Watt’s 1765 steam engine, Stephen Chu illustrates basic principles of thermodynamics -- that energy is conserved, that you can do work from heat, especially when you maximize the difference in temperature in the system and minimize heat dissipation from friction. Chu offers another form of the laws: You can’t win; you can’t break even; and you can’t leave the game.



The game hasn’t changed all that much in the past few centuries. Nations now burn coal for electricity, achieving around 40% thermal efficiency. Natural gas can be harnessed at higher efficiencies still, and if we could deploy temperature-resistant metals for boilers, even less energy would go to waste. This is a pressing matter, points out Chu, because the planet can no longer afford wanton use of carbon-based fuels. With too much CO2, our global “heat engine” has begun to tip toward a point of no return. So the big question for Chu is whether science can design “entropy engines that can generate sustainable (carbon-free) energy sources.



He describes efforts to capture sunlight with improved solar cells, but notes that a silicon shortage, expensive chips, and a learning curve dictated by Moore’s law mean the technology won’t be widely deployed for 10-15 years -- not fast enough in the battle against climate change. Chu likes the efficiencies of power generation from wind, but there’s a limit to turbine size, and the U.S. high voltage transmission network needs a complete and expensive makeover to take full advantage of wind. Forget corn as biofuel, he counsels, since it “barely breaks even in terms of CO2 saved,” and focus instead on perennial grasses like miscanthus. Chu’s lab and others are looking for microbes that can help turn these plants more readily into fuels.



Another potentially rich energy source, Chu says, involves converting sun light into fuel the way plants do in photosynthesis. But “how does nature split water?” asks Chu. Science hasn’t entirely figured out the molecular machinery that turns water into oxygen and hydrogen. Deriving bioenergy through artificial photosynthesis may mean considering entropy and other basic laws in a different light, Chu suggests. “Nature turns out to be very good.”

J.H. Keenan's Contribution to Thermodynamics

Lecture description:

Joseph Henry Keenan, whom this symposium honors, died in 1977, but his groundbreaking work continues to influence the field of thermodynamics, as his colleagues, protégés and scientific descendants attest. Keenan’s efforts had practical outcomes, such as determining the properties of steam, which boosted the electric power industry. But as Ahmed Ghoniem says, Keenan’s exploration and reformulation of the laws of thermodynamics helped place this field in the center of such diverse, contemporary disciplines as the life sciences, energy, information, computation and the nanosciences. “The field has grown from a model of the heat engine to a set of fundamental principles that govern energy conversion in all forms.”



Keenan played a powerful role in MIT’s history as well, notes Susan Hockfield. In Keenan’s 40 years at the Institute, he served as a model teacher. He founded a school of thought and shaped the teaching and application of thermodynamics worldwide. His research “combined developing practical engineering tools with providing explanations of deep subtlety,” and he set a standard for academic leadership, heading the Department of Mechanical Engineering in the difficult post-Sputnik era.



To George Hatsopoulos, Keenan was “my mentor, my friend…His intuition was so unbelievably right; he always led me the right way.” Hatsopoulos shares personal anecdotes about Keenan’s rigorous thinking and precision with language, and offers two short video clips taken by Keenan’s daughter shortly before his death that reveal his method of inquiry. Hatsopoulos suggests that were Keenan alive, he would ask the symposium presenters and audience the following question: “Is entropy an intrinsic property of any system, whether microscopic or macroscopic, whether in a state of equilibrium or nonequilibrium?“

Teaching the Second Law

Lecture description:

Robert Silbey is an old hand at teaching chemistry (40 years and counting), yet each time he turns to the Second Law of Thermodynamics, he’s “always very nervous.” From this panel of educators, we get a sense of how challenging a classroom subject the Second Law can be.



Joseph Smith notes that the teaching approach “depends on the application,” and applications are both theoretical and practical. Students must first ask what is entropy, and why is it needed, says Smith. He focuses on “idealizations that often get ignored,” such as isolation, equilibrium and system boundaries. “If we don’t get those straight in the beginning student’s mind, then there’s a lot of confusion.”



To Howard Butler’s way of thinking, “teaching the Second Law is much more difficult and challenging a task than teaching Newton’s Second Law of Motion,” both because the concepts involved are so much more complex and abstract, and because the Second Law takes on very different forms depending on which thermodynamic domain is being considered.”



Andrew Foley “tries not to worry too much about what entropy is.” Instead, he handles the whole concept as if it were an accounting problem: “money being moved through a mint.” We can “shove the property of energy instead of money, and produce a form of accounting for energy equations.” Says Foley, “First Law, Second Law -- it’s all accounting.”



As engineering and biology converge, “it’s important that students understand the thermodynamics of biological molecules,” says Kim Hamad- Schifferli. She demonstrates the Boltzmann distribution with such biological examples as the coiling of DNA from its double-stranded to single-stranded form. Hamad- Schifferli acknowledges that entropy is very difficult for students to grasp viscerally, and that “one thing that helps greatly is the lattice model -- the entropy of mixing two gases, for example.”



Bernhardt Trout also invokes Boltzmann, “who believed in atoms vehemently, without substantive proof.” This is because “he didn’t want to believe in the soul, he wanted to believe we are nothing but matter and motion.” Trout says that while we can get a more accurate, mathematical description of atoms, “we owe it to our students to teach them about these most fundamental issues to try to reengage the original questions in the original context in which they existed.”



Jeffery Lewins reminisces about being “Keenanized” during his college years. He notes that “in the great book, Professor Keenan uses the energy-entropy volume space quite late to discuss equilibrium.” Lewins suggests that more can be made of this space in teaching.



Enzo Zanchini discusses “a rigorous definition of entropy valid also for nonequilibrium states.” He considers closed systems, and lays out a thorough set of basic definitions, going over the First Law and energy, and the Second Law and entropy.



“There are so many textbooks on thermodynamics, so many schools of thought, says Michael von Spakovsky because “there is not a whole lot of agreement on a lot of things.” He recounts how a unified theory developed at MIT helped resolve key issues in thermodynamics, by proposing “a broader, self-consistent quantum kinematics and dynamics. … Entropy becomes an intrinsic property of matter, including single particles.”

The Perfect Lens: Resolution Beyond the Limits of Wavelength

Lecture description:

According to 1 Corinthians, “For now, we see through a glass, darkly.” But according to Sir John Pendry, now we can actually see through perfectly – not through glass, though. The perfect view is a product of materials science married to theoretical genius, Pendry’s insights into the physics of light and the surprising concept of “negative refraction.”



We have all observed refraction, in the deep end of a swimming pool, for example, where the water looks shallower than it really is. In fact, you can easily calculate the refractive index of water: it’s the actual depth divided by the apparent depth. Unfortunately, that is the only simple mathematical idea in this lecture. The index of refraction in nature is always greater than zero. Building on ideas from Fermat and Maxwell – whose equations, especially the parameters magnetic permeability and electric permittivity, are central to the argument – Pendry uses geometry to persuade us that refraction can in principle be negative. His argument was sharply disputed in the physics literature, and Pendry jokes that he earned his knighthood in combat, using equations as lances.



Why was this controversy so heated? The theory points to a marvelous conclusion: in a material with a refractive index of exactly negative one (-1), the optical distance from an object to its image exactly cancels out. In other words, the image is the object, and therefore we can say that such material functions as a perfect lens. This would enable scientists to defeat a limitation previously considered fundamental: that no lens can resolve more finely than the wavelength of light. Thanks to negative refraction, Sir John claimed, a perfect lens could resolve produce a sharp image of objects smaller than the light used to illuminate them.



Proof came from experiments. Because no natural material demonstrates negative refraction, scientists harnessed metamaterials (a term coined only in 1999). A metamaterial is defined not by its composition but by its structure – a manmade, three-dimensional, periodic cellular architecture designed to produce an optimized response to specific excitation. Researchers at UC San Diego, Boeing, Berkeley, and elsewhere have now produced clear, sharply focused images of text and gratings inscribed at sub-nanometer scales but illuminated at much longer wavelengths.



Pendry emphasizes that negative refraction is still a radically new concept in optics, so truly breakthrough industrial applications have yet to be imagined. But just as the laser developed from a laboratory curiosity to revolutionize medicine and communications, Sir John expects that negative refraction may have enormous potential. “Maybe one of the young grad students in the audience,” he concludes, “will go out and build this stuff, and hopefully make a few billions that he gives back to MIT.”

Death By Black Hole



Lecture topics:

Black Holes Coming to Our Senses. Quantum Mechanics: Defying Common Sense. Importance of Black Holes. Vagabonds of the Solar System. Pluto Not a Planet. Goldie Locks. Satellite Europa. Origins of Life. Death by Black Hole. The Asteroid Apophis: Friday 13th 2029. Man or Robotic Space Travel. Cosmological- Religious Debate. Thought Experiment. Particle Accelerators. Most Relevant Astrophysicist Work.

The Trials of J. Robert Oppenheimer

Movie plot:

J. Robert Oppenheimer was brilliant, arrogant, proud, charismatic — and a national hero. Under his leadership during World War II, the United States succeeded in becoming the first nation to harness the power of nuclear energy to create the ultimate weapon of mass destruction — the atomic bomb. But after the bomb brought the war to an end, in spite of his renown and his enormous achievement, America turned on him, humiliated him, and cast him aside. The question this film asks is, “Why?”

A beautiful new theory of everything

Video description:

Physicist and surfer Garrett Lisi presents a controversial new model of the universe that - just maybe - answers all the big questions. If nothing else, it's the most beautiful 8-dimensional model of elementary particles and forces you've ever seen.

Related Posts

This month I have a bunch of video lectures on thermodynamics and popular-science physics.The thermodynamics videos are exclusively on the 2nd law of thermodynamics, its foundations, teaching, history, and applications in statistical mechanics, quantum physics, cosmology and biophysics.The popular-science physics videos include lectures about black holes, perfect optical lenses, famous physicist Robert Oppenheimer, and theory of everything.This is the 9th post about physics video lectures actually, see the previous eight here: 1 Have fun with these physics video courses and until next time!