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Open AccessArticle

An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration

1
Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 Helsinki, Finland
2
iteratec GmbH, Zettachring 6, 70567 Stuttgart, Germany
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(7), 379; https://doi.org/10.3390/e19070379
Received: 3 July 2017 / Revised: 19 July 2017 / Accepted: 20 July 2017 / Published: 24 July 2017
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field. View Full-Text
Keywords: fluctuation phenomena; random processes; noise and Brownian motion; nonequilibrium and irreversible thermodynamics; control theory; stochastic processes fluctuation phenomena; random processes; noise and Brownian motion; nonequilibrium and irreversible thermodynamics; control theory; stochastic processes
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Muratore-Ginanneschi, P.; Schwieger, K. An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration. Entropy 2017, 19, 379.

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