Geometrical bounds of the irreversibility in classical and open quantum systems

Tan Van Vu, Yoshihiko Hasegawa

Published 2020-05-06Version 1

We derive geometrical bounds on the irreversibility for both classical and open quantum systems that satisfy the detailed balance conditions. Using the information geometry, we prove that the irreversible entropy production is bounded from below by a Wasserstein-like distance between the initial and final states, thus generalizing the Clausius inequality. The Wasserstein-like metric can be regarded as a discrete-state generalization of the Wasserstein metric, which plays an important role in the optimal transport theory. Notably, the derived bounds closely resemble classical and quantum speed limits, implying that the minimum time required to transform a system state is constrained by the associated entropy production.