Extensive increase of entropy in quantum quench

TL;DR

This paper proves that in isolated quantum systems undergoing a nontrivial quantum quench, both thermodynamic and diagonal entropies increase extensively, with the thermodynamic entropy increasing for any initial thermal state and the diagonal entropy for stationary states satisfying the eigenstate thermalization hypothesis.

Contribution

It establishes rigorous proofs of extensive entropy increase in quantum quenches, covering a broad class of initial states and Hamiltonian conditions.

Findings

Thermodynamic entropy increases extensively for any initial thermal equilibrium state.

Diagonal entropy increases extensively for stationary states under eigenstate thermalization hypothesis.

The results apply to nontrivial quantum quenches in isolated quantum systems.

Abstract

In the setup of isolated quantum systems, it is proved that the thermodynamic entropy and the diagonal entropy must increase extensively in any nontrivial quantum quench. The extensive increase of the thermodynamic entropy is shown for any initial state (even for a pure state) that represents thermal equilibrium. On the other hand, the extensive increase of the diagonal entropy is shown for any stationary initial state under the condition that both the pre-quench and the post-quench Hamiltonians satisfy the eigenstate thermalization hypothesis.