Conditional Entropy Production and Quantum Fluctuation Theorem of Dissipative Information: Theory and Experiments

Abstract

We study quantum conditional entropy production, which quantifies the irreversibility of system-environment evolution from the perspective of a third system, called the reference. The reference is initially correlated with the system. We show that quantum unconditional entropy production with respect to the system is less than conditional entropy production with respect to the reference, where the latter includes reference-induced dissipative information. Dissipative information pinpoints the distributive correlation established between the environment and the reference, even though they do not interact directly. When reaching thermal equilibrium, the system-environment evolution has a zero unconditional entropy production. However, one can still have a nonzero conditional entropy production with respect to the reference, which characterizes the informational nonequilibrium of the system-environment evolution from the viewpoint of the reference. The additional contribution to conditional entropy production, dissipative information, characterizes a minimal thermodynamic cost that the system pays to maintain correlation with the reference. Positive dissipative information also characterizes potential work waste. We prove that both types of entropy production and dissipative information follow quantum fluctuation theorems when a two-point measurement is applied. We verify the quantum fluctuation theorem for dissipative information experimentally on IBM quantum computers. We also present examples based on the qubit collisional model and demonstrate universal nonzero dissipative information in the qubit Maxwell’s demon protocol.