Journal
PHYSICAL REVIEW E
Volume 86, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.86.041148
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Funding
- McKnight Foundation
- Hellman Family Faculty Fund
- McDonnell Foundation
- Mary Elizabeth Rennie Endowment for Epilepsy Research
- National Science Foundation [IIS-1219199]
- Office of Basic Energy Sciences of the US Department of Energy [DE-AC02-05CH11231]
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A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one-dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first-order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory.
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