Efficiency at maximum power: An analytically solvable model for stochastic heat engines

2007/10/22 by Tim Schmiedl, Udo Seifert · 15 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Brownian motion #Carnot cycle #Chemistry #Harmonic #Heat engine #Limit (mathematics) #Mathematical analysis #Mathematics #Maximum power principle #Physics #Power (physics) #Quantum mechanics #Simple (philosophy) #Statistics #Thermal efficiency #Thermodynamics #Zero (linguistics) #cond-mat.stat-mech #stochastic dynamics and bifurcation #thermodynamics and calorimetric analyses

paper · pdf · doi:10.1209/0295-5075/81/20003

published as EPL, 81 (2008) 20003 · 6 pages, 3 figures

arxiv created 2007/10/22 · openalex publication_date 2007/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.

Citations

• Entropy Production for Mechanically or Chemically Driven Biomolecules
• Tight coupling in thermal Brownian motors
• Microscopic Analysis of a Thermal Brownian Motor
• Carnot’s cycle for small systems: Irreversibility and cost of operations

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