The definition of the thermodynamic entropy in statistical mechanics

TL;DR

This paper proposes a new definition of thermodynamic entropy based on the time-dependent probability distribution of macroscopic variables, ensuring compliance with the Second Law and thermodynamic postulates.

Contribution

It introduces a probability-based entropy definition that automatically peaks at equilibrium, resolving previous objections and aligning with thermodynamic principles.

Findings

Entropy peaks at equilibrium after constraint release

The definition satisfies the Second Law and thermodynamic postulates

Objections by Dieks and Peters are addressed and resolved

Abstract

A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new equilibrium values goes to a narrow peak. Defining the entropy by the logarithm of the probability distribution automatically makes it a maximum at the equilibrium values, so it satisfies the Second Law. It is also satisfies the postulates of thermodynamics. Objections to this definition by Dieks and Peters are discussed and resolved.