Entropy Production Fluctuations in Quantum Processes

Shubhashis Rana, Sourabh Lahiri, A. M. Jayannavar

Zhiqiang Huang

Entropy production and the detailed fluctuation theorem are of fundamental importance for thermodynamic processes. In this paper we study the multiple entropy production for multitime quantum processes in a unified framework. For closed quantum systems and Markovian open quantum systems, the given entropy productions all satisfy the detailed fluctuation relation. This also shows that the entropy production rate under these processes is non-negative. For non-Markovian open quantum systems, the memory effect can lead to a negative-entropy production rate. Thus, in general, the entropy production of the marginal distribution does not satisfy the detailed fluctuation theorem relation. Our framework can be applied to a wide range of physical systems and dynamics. It provides a systematic tool for studying entropy production and its rate under arbitrary quantum processes.

Lorenzo Pucci, Massimiliano Esposito, Luca Peliti

Gonzalo Manzano, Jordan M. Horowitz, Juan M. R. Parrondo

We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments.First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics.Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin.We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.

Y. Tokura

B. Ahmadi, S. Salimi, A. S. Khorashad

The second law of classical equilibrium thermodynamics, based on the positivity of entropy production, asserts that any process occurs only in a direction that some information may be lost (flow out of the system) due to the irreversibility inside the system. However, any thermodynamic system can exhibit fluctuations in which negative entropy production may be observed. In particular, in stochastic quantum processes due to quantum correlations and also memory effects we may see the reversal energy flow (heat flow from the cold system to the hot system) and the backflow of information into the system that leads to the negativity of the entropy production which is an apparent violation of the Second Law. In order to resolve this apparent violation, we will try to properly extend the Second Law to quantum processes by incorporating information explicitly into the Second Law. We will also provide a thermodynamic operational meaning for the flow and backflow of information. Finally, it is shown that negative and positive entropy production can be described by a quantum thermodynamic force.