On the Numerical Integration of the Fokker–Planck Equation Driven by a Mechanical Force and the Bismut–Elworthy–Li Formula

Entropy, Journal Year: 2025, Volume and Issue: 27(3), P. 218 - 218

Published: Feb. 20, 2025

Optimal control theory aims to find an optimal protocol steer a system between assigned boundary conditions while minimizing given cost functional in finite time. Equations arising from these types of problems are often non-linear and difficult solve numerically. In this article, we describe numerical methods integration for two partial differential equations that commonly arise theory: the Fokker–Planck equation driven by mechanical potential which use Girsanov theorem; Hamilton–Jacobi–Bellman, or dynamic programming, gradient its solution using Bismut–Elworthy–Li formula. The computation is necessary specify protocol. Finally, give example application techniques solving problem without spacial discretization machine learning.

Language: Английский

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Minimal work protocols for inertial particles in nonharmonic traps

Physical review. E, Journal Year: 2025, Volume and Issue: 111(3)

Published: March 25, 2025

Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest problems stochastic thermodynamics, typically concerning a time-dependent potential applied nanoparticle reach target stationary state given time minimal energy cost. We study this problem for particle subject thermal fluctuations regime that takes into account the effects of inertia, and, building on results previous work, we provide numerical method find optimal controls even non-Gaussian initial and final conditions, corresponding nonharmonic confinements. Although focus where driving is long compared characteristic relaxation times dynamics, protocol position distribution are qualitatively different from overdamped limit: particular, symmetry boundary which preserved absence turns out be broken underdamped regime. also show momentum mean tends constant value along trajectory, except close boundary, while evolution second moments highly nontrivial. Our support lower bound entropy production computed case tight adiabatic limit.

Language: Английский

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Learning efficient erasure protocols for an underdamped memory

Physical review. E, Journal Year: 2025, Volume and Issue: 111(4)

Published: April 10, 2025

Language: Английский

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Optimal Control of an Electromechanical Energy Harvester

Entropy, Journal Year: 2025, Volume and Issue: 27(3), P. 268 - 268

Published: March 5, 2025

Many techniques originally developed in the context of deterministic control theory have recently been applied to quest for optimal protocols stochastic processes. Given a system subject environmental fluctuations, one may ask what is best way change its controllable parameters time order maximize, on average, certain reward function, while steering between two pre-assigned states. In this work, we study problem wide class systems, inspired by model an energy harvester. The noise due mechanical vibrations, function average power extracted from them. We consider case which electrical resistance harvester can be changed time, and exploit tools work out solutions perturbative regime, close stationary state. Our results show that it possible design perform better than any solution with constant resistance.

Language: Английский

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Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales

Physical review. E, Journal Year: 2025, Volume and Issue: 111(3)

Published: March 11, 2025

Geometrical methods are extensively applied to thermodynamics, including stochastic thermodynamics. In the case of a slow-driving linear response regime, geometrical framework, known as thermodynamic geometry, is established. The key this framework length characterized by metric tensor defined in space controlling variables. As given terms equilibrium time-correlation functions forces, it contains information on timescales, which may be useful for analyzing performance heat engines. paper, we show that underdamped Langevin dynamics can decomposed relaxation times system itself, govern timescales forces. an application decomposition tensor, demonstrate possible achieve Carnot efficiency at finite power taking vanishing limit without breaking trade-off relations between and engines geometry.

Language: Английский

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Control of friction: Shortcuts and optimization for the rate- and state-variable equation

European Journal of Mechanics - A/Solids, Journal Year: 2024, Volume and Issue: 111, P. 105550 - 105550

Published: Dec. 30, 2024

Language: Английский

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