Fluctuation Theorems for multitime processes

TL;DR

This paper extends fluctuation theorems to multitime quantum processes, accounting for correlations and non-Markovian effects, and provides a unified framework for understanding entropy production in complex quantum systems.

Contribution

It introduces a general quantum fluctuation theorem framework for multitime processes, including many-body channels and non-Markovian effects, with new insights into correlations and measurement strategies.

Findings

Fluctuation theorems apply to multitime quantum processes.

Memory effects can reduce fluctuations in non-Markovian systems.

Intermediate state measurements are extended from two-point to three-point in Markovian cases.

Abstract

In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of a closed system environment. The assumption that the system evolves under a completely positive and trace preserving map is quite general, but it is more specific for cases in which the system is initially correlated with the environment. System-environment correlations arise naturally in multitime processes, with which we can give clear and physical interpretations regarding the effects of correlations. Multitime processes can provide many-body channels. The Choi state of such a many-body channel is called a process tensor. One can derive channels by executing the process tensor on a set of operations. We establish a general quantum fluctuation theorem framework for a many-body channel and its derived channels. In this framework, the effects of correlations are reflected in a Markovian property. For Markovian processes, we can extend the two-point measurement to a three-point measurement and obtain that the fluctuation theorems contain complete information about the intermediate state. For non-Markovian processes, the complete measurement of the intermediate state leads to conflicts. Therefore, we use a general measurement, which only provides partial information, for the intermediate state. The corresponding fluctuation theorems show that memory effects can reduce these fluctuations. This is consistent with the fact that system states can be recovered under non-Markovian processes.