Optimal control of a stochastic oscillator in non-equilibrium thermodynamics

Using a parametrically-controlled stochastic oscillator (a model of a heat engine) as illustration, we bring geometric control theory to non-equilibrium thermodynamics. A problem of optimal control is to find finite-time protocols maximizing efficiency of the heat engine. In the approximation of linear response theory, working cycles of the engine are constrained minimizers of energy dissipation, determined through the Pontryagin maximum principle.

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