Entropy Production in Isolated Quantum Many-Body Systems

Y. Tokura

Kazuya Kaneko, Eiki Iyoda, Takahiro Sagawa

Bridging the second law of thermodynamics and microscopic reversible dynamics has been a longstanding problem in statistical physics. Here, we address this problem on the basis of quantum many-body physics, and discuss how the entropy production saturates in isolated quantum systems under unitary dynamics. First, we rigorously prove that the entropy production does indeed saturate in the long time regime, even when the total system is in a pure state. Second, we discuss the non-negativity of the entropy production at saturation, implying the second law of thermodynamics. This is based on the eigenstate thermalization hypothesis, which states that even a single energy eigenstate is thermal. We also numerically demonstrate that the entropy production saturates at a non-negative value even when the initial state of a heat bath is a single energy eigenstate. Our results reveal fundamental properties of the entropy production in isolated quantum systems at late times.

Lorenzo Pucci, Massimiliano Esposito, Luca Peliti

E. Solano‐Carrillo, Andrew J. Millis

We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second, and third laws of thermodynamics. For weakly coupled subsystems of an isolated system, an expression for the long-time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.

Rikuya Kobashi

We derive thermodynamic speed limits for isolated quantum systems undergoing finite-time unitary driving. The key ingredient is a set of generalized second-law inequalities: for the Gibbs entropy and for several thermodynamically motivated observational entropies, the entropy production is bounded from below by a function of the Vu--Saito quantum Wasserstein distance between the initial and final coarse-grained states. These inequalities yield lower bounds on the operation time in terms of the average entropy-production rate. We apply the framework to system--bath coarse-graining, local-energy coarse-graining, and diagonal entropy, and illustrate the resulting bounds with numerical and analytically solvable examples. Our results provide a thermodynamic characterization of finite-time state transformations in isolated quantum systems and clarify how coarse-grained entropy production constrains macroscopic reachability.

K. Lendi