Emergent Second Law for Time-Dependent Nonequilibrium States

Nahuel Freitas; Timur Aslyamov; Massimiliano Esposito

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arXiv · 2608.21661

Emergent Second Law for Time-Dependent Nonequilibrium States

Nahuel Freitas·Timur Aslyamov·Massimiliano Esposito

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Abstract

For nonautonomous open systems described by macroscopic stochastic thermodynamics, we derive an emergent second law that constrains time-dependent macroscopic fluctuations by the entropy production along the most probable evolution under the time-reversed driving protocol. We show that this bound can be understood as a macroscopic consequence of the fluctuation theorem: the time reverse of this evolution provides a possible fluctuation path under the forward dynamics. In the linear-response and slow-driving regime, the bound becomes an equality to first order and generalizes the McLennan-Zubarev formula to the time-dependent probability density of nonautonomous systems with weak nonconservative affinities. We illustrate our results in a bistable system under sudden quenches and periodic driving.

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Nahuel Freitas, Timur Aslyamov, Massimiliano Esposito. 2026-08-21. Emergent Second Law for Time-Dependent Nonequilibrium States. https://arxiv.org/abs/2608.21661

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