The unlikely Carnot efficiency

Abstract

The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It led to the discovery of the second law and to the definition of the Kelvin temperature scale. Small-scale engines operate in the presence of highly fluctuating input and output energy fluxes. They are therefore much better characterized by fluctuating efficiencies. In this study, using the fluctuation theorem, we identify universal features of efficiency fluctuations. While the standard thermodynamic efficiency is, as expected, the most likely value, we find that the Carnot efficiency is, surprisingly, the least likely in the long time limit. Furthermore the probability distribution for the efficiency assumes a universal scaling form when operating close-to-equilibrium. We illustrate our results analytically and numerically on two model systems.

7 pages, 3 figures, v3: as accepted in Nature Communications

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• Overdamped stochastic thermodynamics with multiple reservoirs
• Constitutive Relation for Nonlinear Response and Universality of Efficiency at Maximum Power for Tight-Coupling Heat Engines
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• Fluctuation Theorem for a Small Engine and Magnetization Switching by Spin Torque
• General relations between the power, efficiency and dissipation for the irreversible heat engines in the nonlinear response regime
• Statistics of heat transport across capacitively coupled double quantum dot circuit
• A kinetic model for the finite-time thermodynamics of small heat engines
• Short time dynamics of molecular junctions after projective measurement
• Testing Time Reversal Symmetry in Artificial Atoms