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The first part of the book starts by presenting the problem thermodynamics is trying to solve, and provides the postulates on which thermodynamics is founded. It then develops upon this foundation to discuss reversible processes, heat engines, thermodynamics potentials, Maxwell's relations, stability of thermodynamics systems, and first-order phase transitions.
The series includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential Equations in Physics. Focusing on one subject each semester, the lectures formed a three-year cycle of courses that Sommerfeld repeatedly taught at the University of Munich for ...
At the same time, Gibbs fully generalized and expanded statistical mechanics into the form in which it is known today. Gibbs showed how statistical mechanics could be used even to extend thermodynamics beyond classical thermodynamics, to systems of any number of degrees of freedom (including microscopic systems) and non-extensive systems.
Thermodynamics and statistical mechanics. {}: CS1 maint: multiple names: authors list Translated by J. Kestin (1956) New York: Academic Press. Ehrenfest, Paul and Tatiana (1912). The conceptual foundations of the statistical approach in mechanics. German Encyclopedia of Mathematical Sciences.
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
It can also be called the statistical entropy or the thermodynamic entropy without changing the meaning. Note the above expression of the statistical entropy is a discretized version of Shannon entropy. The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case.
As this quantity H was meant to represent the entropy of thermodynamics, the H-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics.