Fluctuation theorems in the presence of information gain and feedback

Abstract

In this study, we rederive the fluctuation theorems in the presence of feedback by assuming the known Jarzynski equality and detailed fluctuation theorems. We find that both the classical and quantum systems can be analyzed using a similar treatment in terms of state space trajectories. We first briefly reproduce the already known work theorems for a classical system in order to show its equivalence with the quantum treatment. We then extend the treatment to arrive at new results, namely the generalizations of Seifert’s entropy production theorem and the Hatano–Sasa fluctuation theorem, in the presence of feedback. We have also derived the extended version of the Tasaki–Crooks fluctuation theorem for a quantum particle in the presence of multiple loop feedback. For deriving the extended quantum fluctuation theorems, we have considered open systems. No assumption is made on the nature of environment and the strength of system–bath coupling. However, it is assumed that the measurement process involves classical errors.