Quantum fluctuation theorems and work-energy relationships with due regard for convergence, dissipation and irreversibility

Abstract

Firstly the fluctuation theorems (FT) for expended work in a driven nonequilibrium system, isolated or thermostatted, together with the ensuing Jarzynski work-energy (W-E) relationships, will be discussed and reobtained. Secondly, the fluctuation theorems for entropy flow will be reconsidered. Our treatment will be fully quantum-statistical, being an ex-tension of our previous research reported in Phys. Rev. E (2012), and will avoid the deficiencies that afflicted previous works such as: arguments based on classical trajectories in phase space, a reliance on the 'pure' von Neumann equation or 'non-reduced' Heisenberg operators, or other departures from the general tenets spelled out by Lindblad and others (e.g. Breuer and Petruccione) such as stochastic 'jump-induced' random trajectories. While a number of relationships from such previous works will still be employed, our Markov probability $P(\sigma_f,t_f|\sigma_0,t_0)$ shall only denote the two state-points, with no reference whatsoever to stochastic trajectories, these being meaningless in a quantum description.