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E. T. Jaynes
Edwin Thompson Jaynes extended statistical mechanics to connect it to probability theory, Claude Shannon's information theory, and Bayesian statistical inferences.
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He championed the work of J. Willard Gibbs, contrasting it to the earlier work of Ludwig Boltzmann. His 1957 "principle of maximum entropy" or "maxent" says that the probability distribution that best represents the current state of knowledge is the one with largest entropy. In 1964, Jaynes examined the difference between the Boltzmann and Gibbs formulations of the entropy. They differ, he says, because of different treatments of "interparticle forces." The status of the Gibbs and Boltzmann expressions for entropy has been a matter of some confusion in the literature. We show that:Jaynes explains that Gibbs entropy is a conserved quantity, for the same reason as the Liouville theorem that conserves the hyper-volume in phase space of a cloud of particles as it traverses its trajectory.
Boltzmann entropy increases. We can show that this is a consequence of quantal interactions during particle collisions, which deny the claim of microscopic reversibility and erase the path information in the gas particles that would be needed to support Loschmidt's objection to the Boltzmann In the writer's 1962 Brandeis lectures on statistical mechanics, the Gibbs and Boltzmann expressions for entropy were compared briefly, and it was stated that the Gibbs formula gives the correct entropy, as defined in phenomenological thermodynamics, while the Boltzmann As to the connections between entropy and information, in particular, "subjective human ignorance," Jaynes says, The phase volume W
Gibbs Paradox
In Jaynes' article on the famous paradox, he writes...
Some important facts about thermodynamics have not been understood by others to this day, nearly as well as Gibbs understood them over 100 years ago. Other aspects of this “new” development have been reported elsewhere (Jaynes 1986, 1988, 1989). In the present note we consider the “Gibbs Paradox” about entropy of mixing and the logically inseparable topics of reversibility and the extensive property of entropy.
References
Gibbs vs Boltzmann Entropies,
The Gibbs Paradox, in |