# Nonequilibrium thermodynamics and information theory: Basic concepts and relaxing dynamics

## TL;DR

This paper explores the fundamental links between thermodynamics and information theory, emphasizing how strongly relaxing dynamics underpin irreversible processes and convergence to equilibrium in open systems.

## Contribution

It provides a comprehensive, first-principles framework connecting energy, entropy, and information theory, extending thermodynamic bounds to open and driven systems.

## Key findings

- Thermodynamic inequalities are equivalent to strongly relaxing dynamics.
- Markov processes converging to equilibrium are strongly relaxing.
- The framework generalizes to open and driven systems, offering new thermodynamic bounds.

## Abstract

Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we give a detailed didactic account on the relations between energy and entropy and thus physics and information theory. We show that thermodynamic process inequalities, like the Second Law, are equivalent to the requirement that an effective description for physical dynamics is strongly relaxing. From the perspective of information theory, strongly relaxing dynamics govern the irreversible convergence of a statistical ensemble towards the maximally non-commital probability distribution that is compatible with thermodynamic equilibrium parameters. In particular, Markov processes that converge to a thermodynamic equilibrium state are strongly relaxing. Our framework generalizes previous results to arbitrary open and driven systems, yielding novel thermodynamic bounds for idealized and real processes.