Extended Fluctuation Theorems for Repeated Measurements and Feedback within Hamiltonian Framework

TL;DR

This paper derives extended fluctuation theorems for systems with multiple measurements and feedback under Hamiltonian dynamics, emphasizing the role of forward trajectories and the non-uniqueness of correction terms.

Contribution

It introduces a Hamiltonian framework for extended fluctuation theorems with feedback, highlighting the non-uniqueness of correction terms and the uniqueness of the efficacy parameter.

Findings

Correction terms in the theorems are non-unique.

The efficacy parameter has a unique physical interpretation.

The derivation uses only forward phase space trajectories.

Abstract

We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an expression for the efficacy parameter, we must necessarily use the notion of reverse trajectory. Our results show that the correction term appearing in the exponent of the extended fluctuation theorems are non-unique, whereas the physical meaning of the efficacy parameter is unique.