Nonequilibrium work relations of open quantum systems in one-time measurement scheme

Because of the ambiguity in defining work and heat in open quantum systems, it is challenging to formulate non-equilibrium work relations for general quantum channels, beyond the unital case. To overcome this challenge, here we introduce well-defined notions of quantum heat and work in open quantum systems, based on the notion of guessed state defined by the one-time measurement scheme, as developed in [Phys. Rev. E 94, 010103(R)]. This allows us to derive non-equilibrium work relations for general quantum channels, and formulate a modified maximum work theorem with respect to the defined “guessed” quantum work.