Bayesian Statistical Mechanics/Thermodynamics: Everything new is actually well-forgotten old …

Some 80-90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, has managed to derive a very simple, but ultimately general mathematical formula for heat capacity vs. temperature from the fundamental thermodynamical principles, using what we would nowadays dub a “Bayesian approach to probability”. Moreover, he has successfully applied his result to fit the experimental data for diverse substances in their solid state in a rather broad temperature range. Nevertheless, Linhart’s work was undeservedly forgotten, although it does represent a valid and fresh standpoint on thermodynamics and statistical physics, which may have a significant implication for academic and applied science.

Everybody would ask me, but how about Ed Jaynes, Richard Cox and other great guys ? Remarkably, Linhart quite intuitively adopted the Bayesian-Laplacian view of the probability notion in the times of its total rejection, long before the publication of Bruno de Finetti’s and Richard Cox’s groundbreaking works (Richard Cox was working on his PhD, whereas de Finetti was only about 16 years old – just in the birth year of Ed Jaynes and Peter Landsberg – when the first Linhart’s paper was published). So why nobody knows who George A. Linhart was ? You’ve got me there ! … But I will try to find out more about this outstanding guy and communicate you in my following posts.

Why is this guy can be considered really outstanding ? For several reasons:

1. He wasn’t fascinated with the notion of entropy and started with two DIRECTLY EXPERIMENTALLY MEASURABLE thermodynamical parameters, namely the TEMPERATURE and HEAT CAPACITY. He has related the latter with the probability of achieve a particular macrostate, whereas the former was viewed by him as odds in favor of the reachability of the intrinsically most probable macrostate. Thus, he used what we call after De Finetti the “Dutch book argument”, but not in an abstract theoretical manner – he managed to find the connection between this abstract theoretical construction and the experimentally measurable parameters.

2. Linhart has shown, how the famous Boltzmann-Planck formula for entropy can be mathematically derived starting from experimental facts (and not just postulated, as done usually).

3. The entropy formula derivation by Linhart also demonstrates the intrinsic connection between the entropy and Schrödinger-Brillouin “negentropy” notions.

4. Linhart’s approach allows to bridge a logical gap between the Boltzmann and Gibbs interpretations of statistical mechanics, without applying to “ergodic theories”, but reconsidering the very notion of “thermodynamical equilibrium”.

5. Pursuing the Linhart’s line of thought, it is possible to show not only mathematical, but also physical interconnection between the Boltzmann-Gibbs and Tsallis statistics.

6. Linhart’s ideas pave the way of mathematical derivation of the universal equation of state.

Got interested ? I have placed a paper about this here

Besides, the pertinent full story is accepted for publication as an essay in the Wiley journal “ChemPhysChem”.


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