Universal relations and bounds for fluctuations in quasistatic small heat engines
arXiv:1910.08096 · doi:10.1038/s42005-025-01961-1
Abstract
The efficiency of any heat engine, defined as the ratio of average work output to heat input, is bounded by Carnot's celebrated result. However, this measure is insufficient to characterize the properties of miniaturized heat engines carrying non-negligible fluctuations, and a study of higher-order statistics of their energy exchanges is required. Here, we generalize Carnot's result for reversible cycles to arbitrary order moment of the work and heat fluctuations. Our results show that, in the quasistatic limit, higher-order statistics of a small engine's energetics depend solely on the ratio between the temperatures of the thermal baths. We further prove that our result for the second moment gives universal bounds for the ratio between the variances of work and heat for quasistatic cycles. We test this theory with our previous experimental results of a Brownian Carnot engine and observe the consistency between them, even beyond the quasistatic regime. Our results can be exploited in the design of thermal nanomachines to reduce their fluctuations of work output without marginalizing its average value and efficiency.
arXiv comment28+5 pages, 4+2 figures, published version
References in corpus (48)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- A single-atom heat engine
- The Nonequilibrium Thermodynamics of Small Systems
- Brownian Carnot engine
- Experimental realization of a Szilard engine with a single electron
- Experimental demonstration of quantum effects in the operation of microscopic heat engines
- Levitodynamics: Levitation and control of microscopic objects in vacuum
- Experimental characterization of a spin quantum heat engine
- Ensemble and Trajectory Thermodynamics: A Brief Introduction
- Quantum absorption refrigerator with trapped ions
- A Micrometer-sized Heat Engine Operating Between Bacterial Reservoirs
- A spin heat engine coupled to a harmonic-oscillator flywheel
- The unlikely Carnot efficiency
- Piezoresistive heat engine and refrigerator
- Spontaneous mechanical oscillation of a DC driven single crystal
- Cycling tames power fluctuations near optimum efficiency
- Multidimensional thermodynamic uncertainty relations
- Efficiency statistics at all times: Carnot limit at finite power
- Adiabatic processes realized with a trapped Brownian particle
- Experimental Realization of a Minimal Microscopic Heat Engine
- Universal theory of efficiency fluctuations
- Fluctuation Relation for Quantum Heat Engines and Refrigerators
- Single Particle Stochastic Heat Engine
- Exactly solvable model of stochastic heat engine: Optimization of power, its fluctuations and efficiency
- The Carnot Cycle for Small Systems: Irreversibility and the Cost of Operations
- Experimental evidence of non-Gaussian fluctuations near a critical point
- Work and dissipation fluctuations near the stochastic resonance of a colloidal particle
- Active engines: Thermodynamics moves forward
- Efficiency fluctuations in microscopic machines
- Fluctuation Relation for Heat Engines
- Universal Bounds on Fluctuations in Continuous Thermal Machines
- Work and power fluctuations in a critical heat engine
- Efficiency Statistics and Bounds for Systems with Broken Time-Reversal Symmetry
- Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat engine model
- Geometry of work fluctuations versus efficiency in microscopic thermal machines
- Efficiency of Single Particle Engines
- Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines
- Stochastic Efficiency: Five Case Studies
- Carnot process with a single particle
- Stochastic efficiency of an isothermal work-to-work converter engine
- Stochastic Heat Engine Powered By Active Dissipation
- Efficiency fluctuations of small machines with unknown losses
- A kinetic model for the finite-time thermodynamics of small heat engines
- Efficiency fluctuations in cyclic machines
- Two coupled, driven Ising spin systems working as an Engine
- Relation between fluctuations and efficiency at maximum power for small heat engines
- Transient exchange fluctuation theorems for heat using Hamiltonian framework: Classical and Quantum
- Correlation-enhanced Stability of Microscopic Cyclic Heat Engines