Quantum thermodynamics of boundary time-crystals

TL;DR

This paper investigates the thermodynamic properties of boundary time-crystals in open quantum systems, demonstrating their persistence at any temperature and analyzing heat, work, and entropy production, with implications for quantum sensing.

Contribution

It provides the first detailed thermodynamic analysis of boundary time-crystals at finite temperature, linking thermodynamic quantities to measurable collective operators.

Findings

Time-crystalline phase persists at all temperatures.

Thermodynamic costs of maintaining time-crystals are characterized.

Framework connects thermodynamics with experimental observables.

Abstract

Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the recent years. However, much less is known about their thermodynamic properties, also due to the intrinsic nonequilibrium nature of these phases. Here, we consider the paradigmatic boundary time-crystal system, in a finite-temperature environment, and demonstrate the persistence of the time-crystalline phase at any temperature. Furthermore, we analyze thermodynamic aspects of the model investigating, in particular, heat currents, power exchange and irreversible entropy production. Our work sheds light on the thermodynamic cost of sustaining nonequilibrium time-crystalline phases and provides a framework for characterizing time-crystals as possible resources for, e.g., quantum sensing. Our results may be verified in experiments, for example with trapped ions or superconducting circuits, since we connect thermodynamic quantities with mean value and covariance of collective (magnetization) operators.