Many Faces of Entropy or Bayesian Statistical Mechanics

TL;DR

This paper revisits Linhart's early Bayesian-derived formula for heat capacity, highlighting its simplicity, broad applicability, and potential significance in thermodynamics and statistical physics, which has been historically overlooked.

Contribution

It brings renewed attention to Linhart's forgotten work, emphasizing its generality and potential impact on modern thermodynamics and statistical mechanics.

Findings

Linhart's formula fits experimental data across various substances.

The Bayesian approach offers a fresh perspective on thermodynamic principles.

Historical analysis of Linhart's contributions highlights overlooked scientific insights.

Abstract

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.