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

TL;DR

This paper develops an analytical framework using non-equilibrium Green's functions to analyze heat and work fluctuations in many-body quantum Otto engines, revealing universal bounds and quantum-specific fluctuation relations.

Contribution

It introduces a novel Green's function approach to derive full statistics of heat and work in quantum Otto cycles with many-body media, including fluctuation relations and bounds.

Findings

Fluctuation-dissipation relation for work is violated in quantum regime.

Universal bounds on heat and work fluctuations are established.

Connections to thermodynamic uncertainty relations are demonstrated.

Abstract

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 non-equilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of non-equilibrium 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 obtain Onsager's transport coefficients for the generic Otto cycle and showed 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.