Portal de Periódicos da CAPES

Optimizing the relaxation route with optimal control

2021; American Physical Society; Volume: 3; Issue: 2 Linguagem: Inglês

10.1103/physrevresearch.3.023128

2643-1564

A. Prados,

Quantum Electrodynamics and Casimir Effect

We look into the minimization of the connection time between nonequilibrium steady states. As a prototypical example of an intrinsically nonequilibrium system, a driven granular gas is considered. For time-independent driving, its natural time scale for relaxation is characterized from an empirical (the relaxation function) and a theoretical (the recently derived classical speed limits) point of view. Using control theory, we find that bang-bang protocols (comprising two steps, heating with the largest possible value of the driving and cooling with zero driving) minimize the connecting time. The bang-bang time is shorter than both the empirical relaxation time and the classical speed limit: in this sense, the natural time scale for relaxation is beaten. Information theory quantities stemming from the Fisher information are also analyzed over these optimal protocols. The implementation of the bang-bang processes in numerical simulations of the dynamics of the granular gas show an excellent agreement with the theoretical predictions. Moreover, general implications of our results are discussed for a wide class of driven nonequilibrium systems. Specifically, we show that analogous bang-bang protocols, with a number of bangs equal to the number of relevant physical variables, give the minimum connecting time under quite general conditions.7 MoreReceived 26 July 2020Revised 17 January 2021Accepted 15 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023128Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasKinetic theoryNonequilibrium & irreversible thermodynamicsOptimization problemsPhysical SystemsGranular fluidsNonequilibrium systemsStatistical PhysicsNonlinear Dynamics