W entropy in hard-core system

TL;DR

This paper investigates the behavior of W entropy in a quantum hard-core boson system, revealing that the second law of thermodynamics holds only at large system scales due to quantum effects.

Contribution

It introduces the study of W entropy in quantum systems and explores its relationship with F entropy, providing insights into thermodynamic irreversibility at quantum scales.

Findings

W entropy and F entropy are approximately linearly related.

The regression period of W entropy depends on lattice scale.

Second law validity depends on system size in quantum systems.

Abstract

As predicted by the second law of thermodynamics, the increase of entropy is irreversible in time. However, in quantum mechanics the evolution of quantum states is symmetrical about time-reversal, resulting a contradiction between thermodynamic entropy and quantum entropy. We study the W entropy, which is calculated from the probability distribution of the wave function on Wannier basis, in hard-core boson system. We find that W entropy and F entropy, which is calculated from the probability distribution of the wave function on Fock basis, satisfy an approximately linear relationship and have the same trend. Then, we investigate the evolution of W entropy for various parameters. We calculate the regression period of W entropy and find its dependence on the lattice scale. Our results show that the second law of thermodynamics is not completely valid in quantum mechanics. The behaviour of W entropy obeys the second law of thermodynamics, only when the system scale is large enough.