Finite-time Polytropic Steering Reveals Non-monotonic Irreversibility

Abstract

How irreversibility evolves from slow to fast driving is a central question in nonequilibrium thermodynamics. While near-equilibrium theory predicts increasing irreversibility with driving speed, the corresponding crossover far from equilibrium is not generally resolved within a unified control framework. Here we introduce polytropic steering, in which a prescribed relation between the ensemble energy and a time-dependent control parameter continuously organizes finite-time processes between isothermal and adiabatic limits. A Fokker-Planck formulation makes the construction applicable to general confining potentials, and yields closed-form thermodynamic expressions for a harmonic trap. We find a non-monotonic irreversibility: the entropy generation decreases in both the quasistatic and fast-driving limits and exhibits a maximum at an intermediate protocol duration. The resulting most-irreversible timescale quantifies the competition between thermal relaxation and external driving. We verify the persistence of this behavior in an anharmonic optical-lattice potential and demonstrate how the same steering principle controls power-efficiency trade-offs in finite-time Brownian engines.

arXiv comment9 pages, 4 figures, comments are welcome