A theorem in dynamics of correlations

M. Bönitz

Kun Zhang, Mo-Yang Ni, Hailong Shi +2 more

Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.

Antonella Agodi, Francesco Calogero

Ivan V. Panyukov, Vladislav Yu. Shishkov, E. S. Andrianov

The quantum regression theorem is a powerful tool for calculating the multitime correlators of operators of open quantum systems whose dynamics can be described in Markovian approximation. However, the scope of the quantum regression theorem is limited by a particular time order of the operators in multitime correlators and does not include out-of-time-ordered correlators. In this work, we obtain an adjoint master equation for multitime correlators that applies to out-of-time-ordered correlators. We show that this equation can be derived for various approaches to the description of the dynamics of open quantum systems, such as the global or local approach. We show that the adjoint master equation for multitime correlators is self-consistent. Namely, the final equation does not depend on how the operators are grouped inside the correlator and it coincides with the quantum regression theorem for the particular time ordering of the operators.

T. Gherega, R. Krieg, P.‐G. Reinhard +1 more

Sania Jevtic, Terry Rudolph, David Jennings +3 more

We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem.