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

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http://hdl.handle.net/10138/217879

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Muratore-Ginanneschi , P & Schwieger , K 2017 , ' An Application of Pontryagin's Principle to Brownian Particle Engineered Equilibration ' , Entropy , vol. 19 , no. 7 , 379 . https://doi.org/10.3390/e19070379

Title: An Application of Pontryagin's Principle to Brownian Particle Engineered Equilibration
Author: Muratore-Ginanneschi, Paolo; Schwieger, Kay
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2017-07
Language: eng
Number of pages: 21
Belongs to series: Entropy
ISSN: 1099-4300
URI: http://hdl.handle.net/10138/217879
Abstract: 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.
Subject: fluctuation phenomena
random processes
noise and Brownian motion
nonequilibrium and irreversible thermodynamics
control theory
stochastic processes
THERMODYNAMICS
EQUATION
DUALITY
114 Physical sciences
111 Mathematics
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