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Termodinamikaren garrantzia…#
Thermodynamics in Our Daily Lives April 24, 2019| R. Stephen Berry
R. Stephen Berry is James Franck Distinguished Service Professor Emeritus at the University of Chicago and a 1983 MacArthur Fellow. His work has contributed to the understanding of the atomic origins of freezing, melting, crystallization, and glass formation.
Thermodynamics is a beautiful illustration of how needs of very practical applications can lead to very basic, general concepts and relations, very much in contrast to the view that the practical and applied facets of a science are consequences of prior basic studies. Thermodynamics teaches us that ideas and concepts can flow in either direction, between the basic and the applied. It was the very practical challenge of finding the best, most efficient way to pump water out of tin mines in Cornwall and elsewhere that stimulated the thinking, notably the young French engineer Sadi Carnot, that led us to the very basic, general concepts, even laws of nature, that we call “thermodynamics”.
Traditional, classical thermodynamics is deeply based on the concept that processes and machines have limits to how efficiently they can carry out their tasks, limits that minimize the wasteful losses that all real processes have. And traditional thermodynamics focuses on finding those limits and hence on how best to get real systems to approach those limits. (Any system that would operate at its ideal limit would operate infinitely slowly and one could not tell whether it was going forward or backward. Ideal processes of that sort are called “reversible”.) But we can see how a science evolves by asking new questions, in the case of thermodynamics, of asking how real systems behave and how they differ from those ideal but unreachable ideal limits. When people began to ask those questions, the science of thermodynamics took on a whole new character and direction. “Irreversible thermodynamics” is the name that new direction took on. And when thermodynamics began examining the consequences of operating a system in real time, that new aspect became known as “finite-time thermodynamics”.
Thermodynamics is, in some ways, the science that most influences our daily lives, because we use its concepts and information in the ways we design and operate so many of the devices we take for granted in our daily lives. Heating and cooling systems in our homes and other buildings, engines that power our motor vehicles, even the design of buildings and vehicles, all incorporate information from thermodynamics to make them perform well. However, in contrast to many other sciences, the way it influences our daily lives is much more subtle, even invisible. We are much more aware of what biology is doing for us every day, or what new devices are coming from quantum physics than of how thermodynamics is influencing our daily lives (although quantum physics does lead to novel aspects of thermodynamics).
The primary impact thermodynamics has on our daily lives is the many ways it shows us how to use energy efficiently, and minimize the wastes that inevitably accompany that use. One of the earliest examples appeared at the birth of the subject, when the work by the French engineer Sadi Carnot revealed that the highest temperatures in any cycle driving a heat engine should be as high as possible. Thermodynamics tells us just how important it is to minimize friction and heat losses through the walls of our engines, and it can tell us, for example, what is the best temperature profile for a distillation column to achieve the most efficient performance. It tells us how to build houses that require little or no heating fuel. Hence thermodynamics becomes a guide to design devices that best perform as we would
Fisika estatistikoa, zertarako?#
Almost everything. Unlike Quantum Mechanics or Classical Mechanics, Statistical Mechanics (SM) is an exact science; it is the science of counting. If you can count correctly, you get the correct answer. This enables us to tackle many problems which are almost intractable through direct applications of Classical or Quantum Mechanics. I’ll give a historical account of the application of Statistical Mechanics.
19th Century: The big questions of this time were understanding the properties of ideal gas and the radiation from a black body ( objects which absorb and emit light perfectly.). Application of statistical mechanics in its earliest form led to the theory of Van Der Waals gas. Concepts from that theory was then successfully applied to understand liquefaction of gas.
Black Body Radiation was a big problem. Rayleigh gave a formula which was unable to account for the observed radiation profile. Planck tried to tackle the problem and figured out the Quantum Theory of Radiation. The tool he mainly used was Thermodynamics.
Boltzman is the founding father of the Statistical Mechanics. He applied his theory to understand the entropy. temperature in a much better way. Also, he worked on transport theory. How energy, momentum etc is transported from one place to another place in a system which is out of equilibrium: Boltzmann equation .
Statistical Mechanics was applied to understand the chemistry of colloids, gel etc.
First half of 20th Century Einstein and Debye used Planck’s quantum hypotheses and Equilibrium Statistical Mechanics to understand the heat capacity of the solids. Einstein, Smoluchowski also described Brownian Motion.
Later Debye and Nernst successfully applied SM to understand different electro-chemical phenomena: Peter Debye . Nernst equation
Arrhenius applied SM to understand Chemical Kinetics which is now famously known as Arrhenius Law.
Bose and Fermi discovered their eponymous statistics which is widely used in modern day research. Discovery of Fermi Dirac Statistics ushered the electronics age.
Around the same time S. Chandrasekhar applied FD statistics to understand the physics of White Dwarf stars. The famous result is now known as Chandrasekhar limit .
Frits Zernike used SM to understand physics of liquids around this time.
Landau and Ginzburg started describing phase transition using SM which is now known as Ginzburg–Landau theory of phase transition.
Claude Shannon used SM to understand what do we mean by information. We now know this as Information Theory.
Lars Onsager used SM to solve the 2D Ising model, a simple model which shows ferro/para-magnetic phase transition.
Second half of 20th Century A lot of impetus was given to understand the physics of phase transition. Leo Kadanoff , Michael Fisher and Kenneth G. Wilson elucidated the mechanism of phase transition.
Richard Feynman , Pyotr Kapitsa etc applied SM to understand low temperature physics particularly Superfluidity.
People tried to understand other materials like Polymer, Liquid Crystals, Foam etc. Pierre-Gilles de Gennes , Sam Edwards , Robert B. Meyer etc applied SM to understand these objects. It is due to their research that we have LCD, LED display.
Ilya Prigogine applied it to understand complex non equilibrium phenomenon and thus ushered a new age of non-equilibrium SM.
Presently almost each and every research that is being done involves some amount of SM. Wilson actually showed that a Statistical field theory in d+1 dimension is equivalent to a Quantum Field Theory in d dimension. This enables us to apply SM to virtually any place in science. In recent days people tried to understand exotic forms of matter like High Temperature Superconductivity, Plasma, Neutron Star, Granular Matter. Turbulence, Social Network etc is analyzed using this tool. Like I said initially, it is applied everywhere.
A big achievement in Biophysics was to understand the mechanism of mRNA production (commonly known as transcription). A simple SM model can describe what is possibly happening at the cellular level. These calculations have led to new experimental discovery which were previously thought to be impossible.
Also, around 1975 John Hopfield and Jacques Ninio figured out how protein is synthesized within cell with less than 0.01% error. They figured out a mechanism completely through theoretical calculation which was later proved to be true. This mechanism is known as Kinetic proofreading .
Clearly, this list is not exhaustive, but I tried to give some highlights on the application of SM. Please google for further information.
…egun, askotariko eraginak dauzka Fisika estatistikoak, etorkizuneko lanen bihotzean dago#
Charles H Martin.
PhD & NSF Fellow, Theoretical Chemical Physics, University of Chicago · Upvoted by Shankar Iyer, Core Data Scientist at Facebook and Justin Rising, PhD in statistics ·Stat mech is a very broad field and machine learning overlaps it at a foundational level for many methods including basic methods such as maximum entropy and exponential families, and advanced methods such as transductive learning and deep learning.
I have a blog post on starting stat mech Metric Learning: Some Quantum Statistical Mechanics, in my blog, and I have some examples of how the formalism is used for both music recommendations Music Recommendations and the Logistic Metric Embedding and Transductive learning Machine Learning with Missing Labels: Transductive SVMs
The classic work on the subject is Jayne’s writings, such as Page on wustl.edu
Stat Mech is the foundation of Deep Learning, as discussed in Hinton’s excellent class. He starts off with a very basic method–the Ising model–in the form of Hopfield Networks. Then he discusses how he solved the core problems of inference in these models with RBMs and Contrastive Divergence. He uses core ideas such as defining the temperature dependent logistic function for stochastic units–which is actually the fermi function from stat mech, and applying mean field theory to get the update rules for learning. Of course, Hinton did his PhD under a theoretical chemist, so it makes a lot of sense that he would use these powerful methods
(Stat mech also comes up in graph propagation methods, since the message passing algos they use is actually a known method called the Bethe approximation)
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