Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints

TL;DR

This paper explores how quantum phase transitions influence thermodynamical quantities like work and entropy in mean-field systems, revealing unique critical signatures and irreversibility behaviors during finite-time cycles.

Contribution

It provides analytical expressions linking work statistics and entropy production to mean-field critical exponents and control parameters, highlighting distinct irreversibility features in mean-field critical systems.

Findings

Irreversible work remains constant even with infinitely slow driving.

Negative work probability decreases with longer critical point proximity.

Irreversibility at zero temperature analyzed via coherence relative entropy.

Abstract

Understanding the dynamical consequences of quantum phase transitions on thermodynamical quantities, such as work statistics and entropy production, is one of the most intriguing aspect of quantum many-body systems, pinpointing the emergence of irreversibility to critical features. In this work, we investigate the critical fingerprints appearing in these key thermodynamical quantities for a mean-field critical system undergoing a finite-time cycle, starting from a thermal state at a generic inverse temperature. In contrast to non-zero dimensional many-body systems, the presence of a mean-field critical point in a finite-time cycle leads to constant irreversible work even in the limit of infinitely slow driving. This links with the fact that a slow finite-time cycle results in a constant amount of squeezing, which enables us to derive analytical expressions for the work statistics and irreversible entropy, depending solely on the mean-field critical exponents and the functional form of the control parameter near the critical point. We find that the probability of observing negative work values, corresponding to negative irreversible entropy, is inversely proportional to the time the system remains near to the critical point, and this trend becomes less pronounced the lower the temperature of the initial thermal state. Finally, we determine the irreversibility traits under squeezing generation at zero-temperature using the relative entropy of coherence.