Generalized Finite-time Optimal Control Framework in Stochastic Thermodynamics

Abstract

Optimal processes in stochastic thermodynamics represent a frontier for understanding the control and design of non-equilibrium systems, with broad practical applications in biology, chemistry, and nanoscale/mesoscale systems. Optimal transport theory and thermodynamic geometry have emerged as leading optimal control methodologies, but both rely on slow--driving and close-to-equilibrium assumptions. An optimal control framework in stochastic thermodynamics for finite--time driving remains elusive. Here, we solve an optimal control problem for driving the control parameters of a discrete-state far-from-equilibrium process from an initial to a final value in finite time. Optimal driving protocols are derived that minimize the total finite--time dissipation cost of the driving process. Our framework reveals that discontinuous endpoint jumps are a generic, model-independent physical mechanism that minimizes the optimal driving entropy production --- `geometric thermodynamic far-from-equilibrium shortcuts in swift state-to-state transformations' --- whose importance is further amplified in far-from-equilibrium systems. The thermodynamic and dynamical interpretation of discontinuous endpoint jumps is formulated. An exact mapping between the finite--time and slow--driving optimal control formulations is elucidated, advancing the state of the art in optimal transport theory and thermodynamic geometry, which has been the prevailing paradigm for studying optimal processes in stochastic thermodynamics under slow--driving assumptions. Our framework opens up a broad range of applications to the thermodynamically efficient control of far-from-equilibrium systems in finite time, and thereby a route towards their efficient design principles.