Is There a Unique Physical Entropy? Micro versus Macro

TL;DR

This paper clarifies that the apparent discrepancy between thermodynamic and statistical entropy arises from different contexts and conventions, not from fundamental inconsistencies, emphasizing their compatibility within respective frameworks.

Contribution

It argues that the difference between thermodynamic and statistical entropy is due to pragmatic conventions, not fundamental flaws, reaffirming their compatibility.

Findings

Thermodynamic entropy is extensive, statistical entropy is non-extensive.

Discrepancies are due to conventions, not fundamental physics.

No need to revise basic statistical mechanics formulas.

Abstract

Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical mechanics should be revised, either on the basis of quantum mechanics or on the basis of general and fundamental considerations about the (in)distinguishability of particles. In this article we argue against this response. We show that both the extensive thermodynamic and the non-extensive statistical entropy are perfectly alright within their own fields of application. Changes in the statistical formulas that remove the discrepancy must be seen as motivated by pragmatic reasons (conventions) rather than as justified by basic arguments about particle statistics.