Entropy from scattering in weakly interacting systems

TL;DR

This paper uses perturbation theory to analyze how the von Neumann entropy of a subsystem evolves under weak scattering interactions, identifying conditions that lead to entropy increase.

Contribution

It introduces simple criteria for initial states and S matrices that ensure entropy growth in weakly interacting quantum systems.

Findings

Subsystem entropy increases under certain initial states and S matrices.

Initial states with more correlations than product states meet the criteria.

The results apply to scattering processes with weak short-ranged interactions.

Abstract

Perturbation theory is used to investigate the evolution of the von Neumann entropy of a subsystem of a bipartite quantum system under the action of a unitary matrix, in the limit where that matrix is close to the unit matrix. The physical context for such process would be scattering with weak short-ranged interactions where the unitary matrix is the S matrix. We find surprisingly simple criteria for the initial state and the S matrix that guarantee that the subsystem entropy increases. The class of initial states that meet these criteria are more correlated than simple product states of the subsystems. They form a subclass of the set of all separable states, and they can therefore be assembled by classical processes alone.