Fluctuation theorems for quantum processes

Abstract

We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.