Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint

TL;DR

This paper extends shortcuts to adiabaticity to nonequilibrium systems, revealing a geometric interpretation of entropy production and deriving bounds relating time, entropy, and state distance.

Contribution

It introduces a novel application of shortcuts to adiabaticity to nonequilibrium entropy, with an information geometric perspective and a new trade-off relation.

Findings

Entropy separates into two parts following a Pythagorean theorem.

An information-geometric interpretation of entropy production is established.

A lower bound on entropy leads to a trade-off between time, entropy, and state distance.

Abstract

We apply the method of shortcuts to adiabaticity to nonequilibrium systems. For unitary dynamics, the system Hamiltonian is separated into two parts. One of them defines the adiabatic states for the state to follow and the nonadiabatic transitions are prevented by the other part. This property is implemented to the nonequilibrium entropy production and we find that the entropy is separated into two parts. The separation represents the Pythagorean theorem for the Kullback-Leibler divergence and an information-geometric interpretation is obtained. We also study a lower bound of the entropy, which is applied to derive a trade-off relation between time, entropy and state distance.