H-theorem for Systems with an Interaction Invariant Distribution Function

TL;DR

This paper explores the quantum H-theorem, demonstrating that if a system's diagonal density matrix elements are unaffected by interactions, the quantum channel governing its evolution is unital, linking entropy behavior to channel properties.

Contribution

It establishes a connection between the robustness of diagonal density matrix elements and the unitality of quantum channels in the context of the quantum H-theorem.

Findings

Diagonal elements' robustness implies unital quantum channels.

Unital channels correspond to non-diminishing entropy conditions.

Provides criteria for entropy stability in quantum systems.

Abstract

H-theorem gives necessary conditions for a system to evolve in time with a non-diminishing entropy. In a quantum case the role of H-theorem plays the unitality criteria of a quantum channel transformation describing the evolution of the system's density matrix under the presence of the interaction with an environment. Here, we show that if diagonal elements of the system's density matrix are robust to the presence of interaction the corresponding quantum channel is unital.