Optimisation of an active heat engine

Abstract

Optimisation of heat engines at the micro-scale has applications in biological and artificial nano-technology, and stimulates theoretical research in non-equilibrium statistical physics. Here we consider non-interacting overdamped particles confined by an external harmonic potential, in contact either with a thermal reservoir or with a stochastic self-propulsion force (active Ornstein-Uhlenbeck model). A cyclical machine is produced by periodic variation of the parameters of the potential and of the noise. An exact mapping between the passive and the active model allows us to define the effective temperature $T_{eff}(t)$ which is meaningful for the thermodynamic performance of the engine. We show that $T_{eff}(t)$ is different from all other known active temperatures, typically used in static situations. The mapping allows us to optimise the active engine, whatever are the values of the persistence time or self-propulsion velocity. In particular - through linear irreversible thermodynamics (small amplitude of the cycle) - we give explicit formula for the optimal cycle period and phase delay (between the two modulated parameters, stiffness and temperature) achieving maximum power with Curzon-Ahlborn efficiency. In the quasi-static limit, the formula for $T_{eff}(t)$ simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency. A point - overlooked in recent literature - is made about the difficulty in defining efficiency without a consistent definition of effective temperature.

arXiv comment18 pages, 6 pages, submitted for publication

References in corpus (35)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Active Particles in Complex and Crowded Environments
• A single-atom heat engine
• A bacterial ratchet motor
• A nano heat engine beyond the Carnot limit
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Brownian Carnot engine
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Sedimentation, trapping, and rectification of dilute bacteria
• A Micrometer-sized Heat Engine Operating Between Bacterial Reservoirs
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Virial pressure in systems of active Brownian particles
• Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
• Inertial self-propelled particles
• Adiabatic processes realized with a trapped Brownian particle
• Light-controlled Assembly of Active Colloidal Molecules
• Universal theory of efficiency fluctuations
• Autonomous engines driven by active matter: Energetics and design principles
• Heat, temperature and Clausius inequality in a model for active brownian particles
• Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity
• Active Brownian Heat Engines
• Single Particle Stochastic Heat Engine
• Stochastic Stirling engine operating in contact with active baths
• Active engines: Thermodynamics moves forward
• Thermodynamic cycles with active matter
• Clausius relation for active particles: what can we learn from fluctuations?
• Dynamics-dependent density distribution in active suspensions
• A stochastic heat engine using an active particle
• Onsager coefficients of a Brownian Carnot cycle
• Stochastic Work Extraction in a colloidal heat engine in presence of colored noise
• Extracting maximum power from active colloidal heat engines
• Engineered Swift Equilibration of a Brownian Gyrator
• Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

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• Thermodynamically consistent model of an active Ornstein-Uhlenbeck particle
• Optimal finite-time heat engines under constrained control
• Modeling the Efficiency and Effective Temperature of Bacterial Heat Engines
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• A stochastic Stirling engine powered by an active particle
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