The Second Law of Thermodynamics under Unitary Evolution and External Operations

TL;DR

This paper demonstrates that the diagonal entropy in an isolated quantum system satisfies the second law of thermodynamics when external operations are applied, linking quantum dynamics with thermodynamic irreversibility.

Contribution

It establishes that the diagonal entropy fulfills key thermodynamic properties and explains irreversibility through quantum dynamics and external interventions.

Findings

Diagonal entropy is additive and extensive.

External operations induce thermodynamic irreversibility.

Unitary evolution constrains quantum trajectories.

Abstract

A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, meets the first two requirements and that the third requirement is satisfied if an arbitrary external operation is performed at typical times. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that the Hamiltonian dynamics restricts quantum trajectories under unitary evolution and that the external operation is performed without referring to any particular information about the microscopic state of the system.