Optimal Finite-Time Processes In Stochastic Thermodynamics

2007/01/23 by Tim Schmiedl, Udo Seifert · 395 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Mathematical optimization #Mathematics #Optimal control #Particle (ecology) #Physics #Protocol (science) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Statistical physics #Stochastic differential equation #Thermodynamics #Trap (plumbing) #Work (physics) #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.98.108301

published in Physical Review Letters 98(10), 108301 (American Physical Society) · 4 pages, 1 figure, accepted for publication in Phys. Rev. Lett

arxiv created 2007/01/23 · openalex publication_date 2007/03/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08

Abstract

For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicit solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and at the end of the process.

Citations

• Integral fluctuation theorem for the housekeeping heat
• Path-ensemble averages in systems driven far from equilibrium
• Thermodynamics of a Colloidal Particle in a Time-Dependent Nonharmonic Potential
• Work probability distribution in single-molecule experiments
• Steady-State Thermodynamics of Langevin Systems
• The Nonequilibrium Thermodynamics of Small Systems

Cited by

• Optimal multi-parameter control of trapped active matter
• Control of active field theories at minimal dissipation
• Harnessing non-equilibrium forces to optimize work extraction