Foundations of algorithmic thermodynamics

TL;DR

This paper develops a framework using Gács' algorithmic entropy to analyze thermodynamic properties of physical systems, providing new fluctuation inequalities applicable far from equilibrium.

Contribution

It introduces algorithmic versions of key thermodynamic inequalities, extending the applicability of entropy concepts beyond traditional probabilistic ensembles.

Findings

Proves fluctuation inequalities for measure-preserving dynamical systems.

Derives algorithmic versions of Jarzynski's equality and Landauer's principle.

Shows that algorithmic entropy quantifies a system's work capacity from an individual state.

Abstract

G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables or probabilistic ensembles, rendering it applicable to settings arbitrarily far from equilibrium. For measure-preserving dynamical systems equipped with a Markovian coarse-graining, we prove a number of fluctuation inequalities. These include algorithmic versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics. In general, the algorithmic entropy determines a system's actual capacity to do work from an individual state, whereas the Gibbs-Shannon entropy only gives the mean capacity to do work from a state ensemble that is known a priori.