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arXiv · 2604.25798

Finite-time transitions in optimal control and non-equilibrium relaxation

Jan Meibohm·Samuel Monter·Sarah A. M. Loos·Clemens Bechinger
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Abstract

We theoretically and experimentally study finite-time optimal control of a colloidal particle steered through a spatially inhomogeneous environment, modeled by a position-dependent energetic cost at the final state. The competition between this state-dependent penalty and path-dependent dissipation gives rise to a sharp transition in the control strategy at a critical control duration. We further show that this transition can be linked to a dynamical phase transition in nonequilibrium relaxation after a quench, where the control cost maps onto the rate function governing rare trajectories.

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Jan Meibohm, Samuel Monter, Sarah A. M. Loos, Clemens Bechinger. 2026-04-28. Finite-time transitions in optimal control and non-equilibrium relaxation. https://arxiv.org/abs/2604.25798

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