Fluctuation Theorems for multitime processes

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.

14 pages, 2 figures

References in corpus (4)

• Irreversible entropy production, from quantum to classical
• Operational Markov condition for quantum processes
• Quantum Dynamics as an analog of Conditional Probability
• Relative entropies and their use in quantum information theory

Cited by in corpus (7)

• From time-reversal symmetry to quantum Bayes' rules
• Multiple entropy production for multitime quantum processes
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Quasiprobability fluctuation theorem behind the spread of quantum information
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Process tensor distinguishability measures
• Leggett-Garg inequalities for multitime processes