Path-integral approach to the calculation of the characteristic function of work

Work statistics and thermal phase transitions

Many previous studies have demonstrated that work statistics can exhibit certain singular behaviors in the quantum critical regimes of many-body systems at zero or very low temperatures. However, as the temperature increases, it is commonly believed that such singularities will vanish. Contrary to this common recognition, we report a nonanalytic behavior of the averaged work done, which occurs at finite temperature, in the Dicke model as well as the Lipkin-Meshkov-Glick model subjected to the sudden quenches of their work parameters. It is revealed that work statistics can be viewed as a signature of the thermal phase transition when the quenched parameters are tuned across the critical line that separates two different thermal phases.

Quantum-Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion

Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.