Eur. Phys. J. B (2013) 86: 157
https://doi.org/10.1140/epjb/e2013-40003-x

Regular Article

Quantum Hertz entropy increase in a quenched spin chain

¹ Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
² Institute of Physics, University of Augsburg, 86153 Augsburg, Germany

^a e-mail: michele.campisi@physik.uni-augsburg.de

Received: 2 January 2013
Received in final form: 4 February 2013
Published online: 15 April 2013

Abstract

The classical Hertz entropy is the logarithm of the volume of phase space bounded by the constant energy surface; its quantum counterpart, the quantum Hertz entropy, is Ŝ = k_B ln N̂, where the quantum operator N̂ specifies the number of states with energy below a given energy eigenstate. It has been recently proved that, when an isolated quantum mechanical system is driven out of equilibrium by an external driving, the change in the expectation of its quantum Hertz entropy cannot be negative, and is null for adiabatic driving. This is in full agreement with the Clausius principle. Here, we test the behavior of the expectation of the quantum Hertz entropy in the case when two identical XY spin chains initially at different temperatures are quenched into a single XY chain. We observed no quantum Hertz entropy decrease. This finding further supports the statement that the quantum Hertz entropy is a proper entropy for isolated quantum systems. We further quantify how far the quenched chain is from thermal equilibrium and the temperature of the closest equilibrium.