Echo states for detailed fluctuation theorems

TL;DR

This paper introduces the concept of echo states in the context of detailed fluctuation theorems, linking the entropy production of a process to its transformed dynamics under specific initial conditions.

Contribution

It identifies and characterizes echo states that enable direct relations between entropy production in original and transformed stochastic processes.

Findings

Derived explicit conditions for echo states in stochastic dynamics.

Validated the theoretical results with analytical calculations.

Performed numerical simulations on a quantum dot model.

Abstract

Detailed fluctuation theorems are statements about the probability distribution for the stochastic entropy production along a trajectory. It involves the consideration of a suitably transformed dynamics, such as the time reversed, the adjoint, or a combination of these. We identify specific, typically unique, initial conditions, called echo states, for which the final probability distribution of the transformed dynamics reproduces the initial distribution. In this case the detailed fluctuation theorems relate the stochastic entropy production of the direct process to that of the transformed one. We illustrate our results by an explicit analytical calculation and numerical simulations for a modulated two-state quantum dot.