Entropy augmentation through subadditive excess: information theory in irreversible processes

TL;DR

This paper introduces an information-theoretic approach to entropy in irreversible processes, generalizing classical ideas and enabling more efficient computation without coarse-graining.

Contribution

It develops a novel, more general ansatz based on information theory that explains entropy increase without coarse-graining, extending classical kinetic theory.

Findings

Entropy increases without coarse-graining.

Provides a new framework for simulating irreversible processes.

Generalizes the Boltzmann equation using information theory.

Abstract

Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase the key idea of Maxwell and Boltzmann, the Sto{\ss}zahlansatz, a far more general, abstract ansatz is developed. An increase of the Gibbs-Shannon-von Neumann entropy results without the usual coarse-graining. The mathematical structure of the ansatz also provides avenues for efficient computation and simulation.