Information compressibility, entropy production and approach to steady state in open systems

TL;DR

This paper introduces the concept of information compressibility to analyze how open systems approach steady states, linking microstate changes to energy variations and providing insights into non-equilibrium dynamics.

Contribution

It defines information compressibility and proves its relation to entropy and energy derivatives at steady states, offering a new perspective on non-equilibrium steady states in classical and quantum systems.

Findings

At steady state, second and third derivatives of entropy are proportional to energy derivatives.

The sign of information compressibility influences the time to reach different steady states.

The concept applies to both classical and quantum open systems.

Abstract

We introduce the concept of {\em information compressibility}, $K_I$, which measures the relative change of number of available microstates of an open system in response to an energy variation. We then prove that at the time in which the system reaches a steady state, the second and third time derivatives of the information entropy are proportional to the corresponding time derivatives of the energy, the proportionality constant being $K_I$. We argue that if two steady states with different but same-sign $K_I$ are dynamically connected in a non-adiabatic way it takes a longer time to reach the state with compressibility closer to zero than the reverse. This concept, that applies to both classical and quantum open systems, thus provides insight into the properties of non-equilibrium steady states.