4.2 Article

Optimizing the relaxation route with optimal control

期刊

PHYSICAL REVIEW RESEARCH
卷 3, 期 2, 页码 -

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AMER PHYSICAL SOC
DOI: 10.1103/PhysRevResearch.3.023128

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  1. FEDER/Ministerio de Ciencia e Innovacion-Agencia Estatal de Investigacion (Spain) [PGC2018-093998-B-I00]

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By utilizing control theory and information theory, this study shows that the use of bang-bang protocols can minimize the connection time in a granular gas system, surpassing the natural relaxation time scale. Experimental results demonstrate excellent agreement with theoretical predictions, indicating the applicability of this approach to a wide range of driven nonequilibrium systems under certain conditions.
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.

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