Optimizing the relaxation route with optimal control
|Author||Prados Montaño, Antonio|
|Department||Universidad de Sevilla. Departamento de Física Atómica, Molecular y Nuclear|
|Abstract||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 ...
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.
|Funding agencies||Agencia Estatal de Investigación. España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
|Citation||Prados Montaño, A. (2021). Optimizing the relaxation route with optimal control. Physical Review Research, 3 (2), 023128.|