Convergence of macrostates under reproducible processes

TL;DR

This paper proves that in any reproducible macroscopic process, the distinguishability between macrostates, measured by relative entropy, always decreases, extending the second law of thermodynamics to a broader context.

Contribution

It introduces a general proof that mutual distinguishability of macrostates diminishes under any reproducible process, regardless of linearity or nonlinearity.

Findings

Mutual distinguishability decreases in all reproducible processes.

The result extends the second law beyond traditional entropy measures.

Monotonicity of quantum relative entropy under coarse grainings is key.

Abstract

I show that whenever a system undergoes a reproducible macroscopic process the mutual distinguishability of macrostates, as measured by their relative entropy, diminishes. This extends the second law which regards only ordinary entropies, and hence only the distinguishability between macrostates and one specific reference state (equidistribution). The new result holds regardless of whether the process is linear or nonlinear. Its proof hinges on the monotonicity of quantum relative entropy under arbitrary coarse grainings, even those that cannot be represented by completely positive maps.