arXiv subjects

Samuel Monter

Publications and source records attributed to Samuel Monter.

4 recordsLinked to original sources

arXiv2026

Equivalence classes of finite-time transitions in optimal control and non-equilibrium relaxation

We present a theory for the optimal control of stochastic systems in structured environments, represented by penalty terms in the cost functional. We show that such control problems generically feature sharp finite-time transitions associated with a qualitative change in the control strategy at a critical time. Starting from an overdamped Langevin equation and a quadratic cost functional, we show that all resulting problems fall into three canonical equivalence classes (parabolic, hyperbolic, and elliptic), distinguished by the sign of the determinant of the control Hamiltonian. For each class, we obtain the optimal protocol, the cost function, and the critical time in closed form, and show that the transition exhibits features of a continuous phase transition at mean-field level. We then establish a mapping between the optimal control cost and the large-deviation rate function governing non-equilibrium relaxation after a potential quench. The mapping covers the parabolic and hyperbolic classes, while the elliptic class has no simple relaxation counterpart. This correspondence implies that recently discovered finite-time dynamical phase transitions, which are exponentially costly to sample directly, are accessible through ordinary averages over optimally controlled trajectories. To validate our theoretical findings, we report three experiments with optically trapped colloidal particles: a control transition for the mean stochastic work, and the finite-time dynamical phase transitions in free diffusion and in harmonic relaxation.

cond-mat.stat-mech↗

arXiv2026

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

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.

cond-mat.stat-mech↗

arXiv2026

Energy-Efficient Control of Interacting Microscopic Systems: When Longer Paths Save Energy

We experimentally and theoretically study the thermodynamically optimal control of interacting multiple-particle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that transport the system between prescribed trap configurations within a fixed time in the most energy efficient way. For Markovian systems with conservative pairwise interactions, we establish a general result in the low-noise limit: optimal particle trajectories are linear in space and time, corresponding to steady straight-line motion, irrespective of the specific interaction potential, even for nonlinear forces. Thus, conservative interactions do not modify the geometry of the optimal paths. This property breaks down in the presence of strong noise or nonconservative interactions. For the paradigmatic case of hydrodynamic coupling, we demonstrate experimentally that optimal control can involve curved trajectories that significantly reduce the energetic cost by exploiting collectively generated fluid flows. The emergence of curved paths as optimal solutions highlights a fundamental distinction between non-interacting and interacting systems and reveals a cooperative mechanism for energy-efficient control.

cond-mat.soft↗

arXiv2023

Universal symmetry of optimal control at the microscale

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here we investigate experimentally and theoretically the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimal. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.

cond-mat.soft↗