Bounds on fluctuations for machines with broken time-reversal symmetry: A linear response study

Full statistics of nonequilibrium heat and work for many-body quantum Otto engines and universal bounds: A nonequilibrium Green's function approach

We consider a generic four-stroke quantum Otto engine consisting of two unitary and two thermalization strokes with an arbitrary many-body working medium. Using the Schwinger-Keldysh nonequilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of nonequilibrium work and heat. The obtained result is valid up to the second order of the external driving amplitude. We then focus on the linear response limit and obtained Onsager's transport coefficients for the generic Otto cycle and show that the traditional fluctuation-dissipation relation for the total work is violated in the quantum domain, whereas for heat it is preserved. This leads to remarkable consequences in obtaining universal constraints on heat and work fluctuations for engine and refrigerator regimes of the Otto cycle and further allows us to make connections to the thermodynamic uncertainty relations. These findings are illustrated using a paradigmatic model that can be feasibly implemented in experiments.

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.