Distinguishing between Clausius, Boltzmann and Pauling Entropies of Frozen Non-Equilibrium States.

Rainer Feistel

doi:10.3390/e21080799

Abstract

In conventional textbook thermodynamics, entropy is a quantity that may be calculated by different methods, for example experimentally from heat capacities (following Clausius) or statistically from numbers of microscopic quantum states (following Boltzmann and Planck). It had turned out that these methods do not necessarily provide mutually consistent results, and for equilibrium systems their difference was explained by introducing a residual zero-point entropy (following Pauling), apparently violating the Nernst theorem. At finite temperatures, associated statistical entropies which count microstates that do not contribute to a body’s heat capacity, differ systematically from Clausius entropy, and are of particular relevance as measures for metastable, frozen-in non-equilibrium structures and for symbolic information processing (following Shannon). In this paper, it is suggested to consider Clausius, Boltzmann, Pauling and Shannon entropies as distinct, though related, physical quantities with different key properties, in order to avoid confusion by loosely speaking about just “entropy” while actually referring to different kinds of it. For instance, zero-point entropy exclusively belongs to Boltzmann rather than Clausius entropy, while the Nernst theorem holds rigorously for Clausius rather than Boltzmann entropy. The discussion of those terms is underpinned by a brief historical review of the emergence of corresponding fundamental thermodynamic concepts.

Highlights

In 2019, the Rostock University is celebrating the 600th anniversary of its foundation, as the oldest such institution in the Baltic Sea region
Zero-point entropy exclusively belongs to Boltzmann rather than Clausius entropy, while the Nernst theorem holds rigorously for Clausius rather than Boltzmann entropy
At that time Einstein [4] had been the first scientist who seriously considered the possible existence of a residual zero-point entropy of certain crystals at equilibrium (Gutzow and Schmelzer [5,6,7], see Appendix B)

Summary

Introduction

In 2019, the Rostock University is celebrating the 600th anniversary of its foundation, as the oldest such institution in the Baltic Sea region On this occasion, a special silver medal has been issued recently (Figure 1). Another method is by analysing the crystal lattice of the metal and estimating the number of Entropy 2019, 21, 799; doi:10.3390/e21080799 www.mdpi.com/journal/entropy. (Planck adjusting this adjusting constant may to a vanishing entropy, commonly known as the 3rdknown law of [8]) This lead constant may lead zero-point to a vanishing zero-point entropy, commonly thermodynamics, or the Nernst theorem, that had been formulated by Planck [9]. In in as the 3rd law of thermodynamics, or the Nernst theorem, that had been formulated by going beyond the original

Section

Clausius

Boltzmann Entropy

Pauling Entropy

Conclusions