Entropic anomaly and maximal efficiency of microscopic heat engines

Abstract

The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We show that, as a consequence of the recently discovered entropic anomaly, quasi-static engines, whose efficiency is maximal in a fluid at uniform temperature, have in fact vanishing efficiency in presence of temperature gradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured.

Supplementary Information provided as a separate pdf file. Follow the Other formats link

References in corpus (5)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Fluctuation Relations for Diffusion Processes
• Anomalous thermodynamics at the micro-scale
• Inertial effects in B{ü}ttiker-Landauer Motor and Refrigerator at the Overdamped Limit

Cited by in corpus (19)

• Adiabatic processes realized with a trapped Brownian particle
• Experimental Realization of a Minimal Microscopic Heat Engine
• Multiple-scale stochastic processes: decimation, averaging and beyond
• Heat, temperature and Clausius inequality in a model for active brownian particles
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Engineered Swift Equilibration of a Brownian Gyrator
• Fast forward approach to stochastic heat engine
• Finite-time adiabatic processes: derivation and speed limit
• Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator
• Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine
• Functionals in stochastic thermodynamics: how to interpret stochastic integrals
• Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols
• Entropy production of a Brownian ellipsoid in the overdamped limit
• Measuring kinetic energy changes in the mesoscale with low acquisition rates
• Quantifying the validity and breakdown of the overdamped approximation in stochastic thermodynamics: Theory and experiment
• The Heat Distribution of the Underdamped Langevin Equation
• Unattainability of Carnot efficiency in thermal motors: Coarse-graining and entropy production of Feynman-Smoluchowski ratchet
• Entropy Anomaly in Langevin-Kramers Dynamics with a Temperature Gradient, Matrix Drag, and Magnetic Field
• Brownian magneto-gyrator as a tunable microengine