The mutual co-implication of thermodynamics' first and second laws

TL;DR

This paper explores a novel microscopic link between the first and second laws of thermodynamics, showing how each law implies the other through changes in microstate probabilities within a statistical mechanics framework.

Contribution

It uncovers a previously unexplored microscopic connection between thermodynamics' first and second laws using information measures and probability distributions.

Findings

The first and second laws are mutually implied at the microscopic level.

A process $p_i o p_i+dp_i$ links the two laws.

The connection depends on the choice of entropic measure.

Abstract

In classical phenomenological thermodynamics the first and second laws can be regarded as independent statements. Statistical mechanics provides a microscopic substratum that explains thermodynamics in probabilistic terms via a microstate probability distribution ${p_i}$. We study here a hitherto unexplored microscopic connection between the two laws. Given an information measure (or entropic form), each of the two laws implies the other through the process $p_i \to p_i+dp_i$.