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

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.

6 pages, 3 figures

References in corpus (11)

• Brownian motors: noisy transport far from equilibrium
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Optimal finite-time processes in stochastic thermodynamics
• Energy Transduction of Isothermal Ratchets: Generic Aspects and Specific Examples Close to and Far from Equilibrium
• Exact microscopic analysis of a thermal Brownian motor
• Inattainability of Carnot efficiency in the Brownian heat engine
• Feynman's ratchet and pawl: an exactly solvable model
• Rectification of Fluctuations in an Underdamped Ratchet
• The Carnot Cycle for Small Systems: Irreversibility and the Cost of Operations
• Tight coupling in thermal Brownian motors
• Entropy production for mechanically or chemically driven biomolecules

Cited by in corpus (302)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Quantum Thermodynamics
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Efficiency at maximum power of low dissipation Carnot engines
• High-precision test of Landauer's principle in a feedback trap
• Universality of efficiency at maximum power
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Stochastic thermodynamics under coarse-graining
• Second law and Landauer principle far from equilibrium
• The quantum harmonic Otto cycle
• Thermoelectric efficiency at maximum power in a quantum dot
• Most efficient quantum thermoelectric at finite power output
• Quantum-dot Carnot engine at maximum power
• A Micrometer-sized Heat Engine Operating Between Bacterial Reservoirs
• Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist's perspective
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Refined Second Law of Thermodynamics for fast random processes
• Efficiency of heat engines coupled to nonequilibrium reservoirs
• Engineered swift equilibration of a Brownian particle
• Cycling tames power fluctuations near optimum efficiency
• Stochastic resetting: A (very) brief review
• Slow dynamics and thermodynamics of open quantum systems
• Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
• Efficiency at maximum power of minimally nonlinear irreversible heat engines
• Unified thermodynamic uncertainty relations in linear response
• Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• An all-optical nanomechanical heat engine
• Optimal cycles for low-dissipation heat engines
• Efficiency statistics at all times: Carnot limit at finite power
• Efficiency of autonomous soft nano-machines at maximum power
• Efficiency of molecular motors at maximum power
• Magnon-driven quantum-dot heat engine
• Hybrid Microwave-Cavity Heat Engine
• Thermodynamic Geometry of Microscopic Heat Engines
• Optimal working conditions for thermoelectric generators with realistic thermal coupling
• Adiabatic processes realized with a trapped Brownian particle
• Optimal refrigerator
• Identifying optimal cycles in quantum thermal machines with reinforcement-learning
• Periodic Thermodynamics of Open Quantum Systems
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Onsager coefficients of a finite-time Carnot cycle
• Experimental Realization of a Minimal Microscopic Heat Engine
• Universal theory of efficiency fluctuations
• Finite time thermodynamics for a single level quantum dot
• Autonomous engines driven by active matter: Energetics and design principles
• Thermoelectric efficiency of three-terminal quantum thermal machines
• Levitated Nanoparticles for Microscopic Thermodynamics - A Review
• Entropic bounds on currents in Langevin systems
• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• Maximum-power quantum-mechanical Carnot engine
• Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators
• Efficiency at Maximum Power of Laser Quantum Heat Engine Enhanced by Noise-Induced Coherence
• Power-efficiency-dissipation relations in linear thermodynamics
• A generalization of the thermodynamic uncertainty relation to periodically driven systems
• Onsager coefficients in periodically driven systems
• Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
• Geometric optimisation of quantum thermodynamic processes
• Erasure without work in an asymmetric, double-well potential
• Thermoelectric properties of an interacting quantum dot-based heat engine
• Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity
• Optimal performance of periodically driven, stochastic heat engines under limited control
• Efficiency at maximum power output of linear irreversible Carnot-like heat engines
• Active Brownian Heat Engines
• Universal constraint for efficiency and power of a low-dissipation heat engine
• Shortcuts to isothermality and nonequilibrium work relations
• Single Particle Stochastic Heat Engine
• Finite-time erasing of information stored in fermionic bits
• Maximum Efficiency of Low-Dissipation Heat Engines at Arbitrary Power
• Stochastic Stirling engine operating in contact with active baths
• Exactly solvable model of stochastic heat engine: Optimization of power, its fluctuations and efficiency
• Efficiency of a Brownian information machine
• Shortcuts to adiabaticity using flow fields
• Efficiency at and near Maximum Power of Low-Dissipation Heat Engines
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Molecular kinetic analysis of a finite-time Carnot cycle
• Efficiency at maximum power output of quantum heat engines under finite-time operation
• Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines
• Efficiency at maximum power of thermally coupled heat engines
• Active engines: Thermodynamics moves forward
• Phase transition in protocols minimizing work fluctuations
• Powerful energy harvester based on resonant-tunneling quantum wells
• Stochastically driven single level quantum dot: a nano-scale finite-time thermodynamic machine and its various operational modes
• Maximum efficiency of steady-state heat engines at arbitrary power
• Work Output and Efficiency at Maximum Power of Linear Irreversible Heat Engines Operating with a Finite-Sized Heat Source
• Maximum power and corresponding efficiency for two-level heat engines and refrigerators: optimality of fast cycles
• Thermodynamic cycles with active matter
• Coefficient of performance under optimized figure of merit in minimally nonlinear irreversible refrigerator
• Irreversibilities and efficiency at maximum power of heat engines: illustrative case of a thermoelectric generator
• Collective performance of a finite-time quantum Otto cycle
• Violation of TUR in a periodically driven work-to-work converter from weak to strong dissipation
• Experimental validation of the $1/\tau$ -scaling entropy generation in finite-time thermodynamics with dry air
• Internal dissipation and heat leaks in quantum thermodynamic cycles
• Low-dissipation Carnot-like heat engines at maximum efficient power
• On the efficiency at maximum cooling power
• A mechanical autonomous stochastic heat engine
• A stochastic heat engine using an active particle
• Universal features in the efficiency of ultra hot quantum Otto engines
• Minimal model of a heat engine: An information theory approach
• Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction
• Speed-ups to isothermality: Enhanced quantum thermal machines through control of the system-bath coupling
• Brownian motion of a circle swimmer in a harmonic trap
• Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation
• Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat engine model
• A geometric bound on the efficiency of irreversible thermodynamic cycles
• Optimal thermodynamic control in open quantum systems
• Onsager coefficients of a Brownian Carnot cycle
• Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines
• Current fluctuations in periodically driven systems
• From local force-flux relationships to internal dissipations and their impact on heat engine performance: The illustrative case of a thermoelectric generator
• Physically consistent numerical solver for time-dependent Fokker-Planck equations
• Efficiency of a thermodynamic motor at maximum power
• Optimal operating protocol to achieve efficiency at maximum power of heat engines
• Fluctuations in heat engines
• Thermal bath Engineering for Swift Equilibration
• Continuity and boundary conditions in thermodynamics: From Carnot's efficiency to efficiencies at maximum power
• Underdamped Active Brownian Heat Engine
• Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics
• Constitutive Relation for Nonlinear Response and Universality of Efficiency at Maximum Power for Tight-Coupling Heat Engines
• Realization of nonequilibrium thermodynamic processes using external colored noise
• Boosting the performance of the Quantum Otto heat engines
• Optimal work in a harmonic trap with bounded stiffness
• Qubit absorption refrigerator at strong coupling
• Efficiency at maximum power of a quantum Otto engine: Both within finite-time and irreversible thermodynamics
• Heat engines at optimal power: Low-dissipation versus endoreversible model
• Diverging, but negligible power at Carnot efficiency: theory and experiment
• Extracting maximum power from active colloidal heat engines
• Coarse-grained entropy production with multiple reservoirs: unraveling the role of time-scales and detailed balance in biology-inspired systems
• Geodesic path for the minimal energy cost in shortcuts to isothermality
• Efficiency and power of a thermoelectric quantum dot device
• Geometric optimization of non-equilibrium adiabatic thermal machines and implementation in a qubit system
• Connection between maximum-work and maximum-power thermal cycles
• Engineered Swift Equilibration of a Brownian Gyrator
• Second law for active heat engines
• Universality of energy conversion efficiency for optimal tight-coupling heat engines and refrigerators
• Geometric Heat Engines Featuring Power that Grows with Efficiency
• Pareto-optimal cycles for power, efficiency and fluctuations of quantum heat engines using reinforcement learning
• A minimal model of an autonomous thermal motor
• Fast forward approach to stochastic heat engine
• Finite-time adiabatic processes: derivation and speed limit
• Optical tweezers as a mathematically driven spatio-temporal potential generator
• Efficiency at maximum power for classical particle transport
• Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator
• Thermodynamics of stochastic Turing machines
• Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines
• Optimal finite-time Brownian Carnot engine
• Stochastic thermodynamics of self-oscillations: the electron shuttle
• Carnot process with a single particle
• Abstract models for heat engines
• Approaching Carnot efficiency at maximum power in linear response regime
• Maximum power heat engines and refrigerators in the fast-driving regime
• Tuning the performance of a micrometer-sized Stirling engine through reservoir engineering
• Entropic anomaly and maximal efficiency of microscopic heat engines
• Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems
• From thermal rectifiers to thermoelectric devices
• Szilard engines and information-based work extraction for active systems
• Thermodynamic interpretation of Wasserstein distance
• Linear irreversible heat engines based on the local equilibrium assumptions
• Minimal Energy Cost to Initialize a Quantum Bit with Tolerable Error
• Two-Stroke Optimization Scheme for Mesoscopic Refrigerators
• Driven probe under harmonic confinement in a colloidal bath
• Stochastic Heat Engine Powered By Active Dissipation
• Maximal power for heat engines: role of asymmetric interaction times
• Double quantum dot coupled to a quantum point contact: A stochastic thermodynamics approach
• Optimal potentials for temperature ratchets
• Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine
• Optimality of non-conservative driving for finite-time processes with discrete states
• Thermodynamics of one and two-qubit nonequilibrium heat engines running between squeezed thermal reservoirs
• A Brownian cyclic engine operating in a viscoelastic active suspension
• Stochastic thermodynamics for a periodically driven single-particle pump
• Revisiting Feynman's ratchet with thermoelectric transport theory
• Heat leakage in overdamped harmonic systems
• Optimisation of an active heat engine
• A microscopic theory of Curzon-Ahlborn heat engine
• Obtaining efficient thermal engines from interacting Brownian particles under time dependent periodic drivings
• Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes
• Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions
• Work needed to drive a thermodynamic system between two distributions
• Universal efficiency at optimal work with Bayesian statistics
• Optimal protocols and universal time-energy bound in Brownian thermodynamics
• Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols
• True nature of the Curzon-Ahlborn efficiency
• Quantum jump approach to microscopic heat engines
• Work extraction and performance of colloidal heat engines in viscoelastic baths
• Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines
• Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction
• Thermal brachistochrone for harmonically confined Brownian particles
• Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations
• Efficiency at maximum power of a Carnot quantum information engine
• Measuring kinetic energy changes in the mesoscale with low acquisition rates
• Thermodynamics of a stochastic twin elevator
• On the efficiency of heat engines at the micro-scale and below
• Feynman-Smoluchowski engine at high temperatures and the role of constraints
• Nonuniversality of heat engine efficiency at maximum power
• Closed-loop approach to thermodynamics
• Engineered swift equilibration for arbitrary geometries
• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• Exactly solvable model of a passive Brownian heat engine and its comparison with active engines
• Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine
• Coefficient of performance at maximum χ-criterion for Feynman ratchet as a refrigerator
• Subharmonic oscillations in stochastic systems under periodic driving
• Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines
• General relations between the power, efficiency and dissipation for the irreversible heat engines in the nonlinear response regime
• Optimization of stochastic thermodynamic machines
• Optimizing Brownian heat engine with shortcut strategy
• Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink
• Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
• Optimal finite-time heat engines under constrained control
• Achieving Carnot efficiency in a finite-power Brownian Carnot cycle with arbitrary temperature difference
• Quality control by a mobile molecular workshop: quality versus quantity
• The Heat Distribution of the Underdamped Langevin Equation
• Efficiency at maximum power of thermochemical engines with near-independent particles
• Maximum efficiency of low-dissipation refrigerators at arbitrary cooling power
• Performance optimization of low-dissipation thermal machines revisited
• Hidden symmetries and nonlinear constitutive relations for tight-coupling heat engines
• Bernoulli's formula and Poisson's equations for a confined quantum gas: Effects due to a moving piston
• Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle
• Underdamped stochastic thermodynamic engines in contact with a heat bath with arbitrary temperature profile
• Microscopic low-dissipation heat engine via shortcuts to adiabaticity and shortcuts to isothermality
• Proposal of a realistic stochastic rotor engine based on electron shuttling
• Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of states
• Microscopic thermal machines using run-and-tumble particles
• Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics
• The interplay between cycle geometry and performance of sudden refrigerators
• Instantaneous equilibrium Transport for Brownian systems under time-dependent temperature and potential variations: Reversibility, Heat and work relations, and Fast Isentropic process
• Energy pumping in electrical circuits under avalanche noise
• Nonergodic Brownian oscillator
• Gaussian white noise as a resource for microscopic engines
• Kinetic analysis of a chiral granular motor
• Optimized finite-time information machine
• Molecular kinetic analysis of a local equilibrium Carnot cycle
• Estimating performance of Feynman's ratchet with limited information
• Global linear-irreversible principle for optimization in finite-time thermodynamics
• Interaction effect on reservoir-parameter-driven adiabatic charge pumping via a single-level quantum dot system
• Compatibility of Carnot efficiency with finite power in an underdamped Brownian Carnot cycle in small temperature-difference regime
• Ignorance based inference of optimality in thermodynamic processes
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine
• Energy transmutation in nonequilibrium quantum systems
• Maximum efficiency of absorption refrigerators at arbitrary cooling power
• Stochastic thermodynamics of nonharmonic oscillators in high vacuum
• Relation between fluctuations and efficiency at maximum power for small heat engines
• Efficiency of a microscopic heat engine subjected to stochastic resetting
• Active particles in moving traps: minimum work protocols and information efficiency of work extraction
• A linear nonequilibrium thermodynamics approach to optimization of thermoelectric devices
• Enantiomer detection via Quantum Otto cycle
• Gambling Carnot Engine
• Thermodynamics of majority-logic decoding in information erasure
• Maximum efficiency of low-dissipation heat pumps at given heating load
• Partially Observable Szilard Engines
• Optimized efficiency at maximum $\dot{\Omega }$ figure of merit and efficient power of Power law dissipative Carnot like heat engines
• Correlation-enhanced Stability of Microscopic Cyclic Heat Engines
• Reinforcement Learning Approach to Shortcuts between Thermodynamic States with Extra Constraints
• Coupled autonomous thermal machines and efficiency at maximum power
• Shortcuts To Adiabaticity for Lévy processes in harmonic traps
• Optimal engine performance using inference for non-identical finite source and sink
• Characterization and optimization of heat engines: Pareto-optimal fronts and universal features
• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Efficiency at the maximum power of the power law dissipative Carnot-like Heat engines with non-adiabatic dissipation
• Operating conditions and thermodynamic bounds of dual radiative heat engines
• Retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Geodesic path for the optimal nonequilibrium transition: Momentum-independent protocol
• Single Particle Thermodynamics with Levitated Nanoparticles
• Realization of all-optical underdamped stochastic Stirling engine
• Photovoltaic efficiency at maximum power of a quantum dot molecule
• Power-efficiency trade-off for finite-time quantum harmonic Otto heat engine via phase-space approach
• Efficiency at maximum power output for an engine with a passive piston
• Bounds and phase diagram of efficiency at maximum power for tight-coupling molecular motors
• A Numerical Method to Find the Optimal Thermodynamic Cycle in Microscopic Heat Engine
• Optimization of a class of heat engines with explicit solution
• Operational characteristics of single particle heat engines and refrigerators with time asymmetric protocol
• Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport
• Efficiency estimation for an equilibrium version of Maxwell refrigerator
• Foundations of Stochastic Thermodynamics
• Power-Efficiency Constraint for Chemical Motors
• Spectral BBGKY: a scalable scheme for nonlinear Boltzmann and correlation kinetics
• Exactly solvable diffusions from space-time transformations
• Quantum transport phenomena induced by time-dependent fields
• Maximal power output of a stochastic thermodynamic engine
• A stochastic Stirling engine powered by an active particle
• Maximum power Stirling-like heat engine with a harmonically confined Brownian particle
• Phase shift in periodically driven non-equilibrium systems: Its identification and a bound
• Optimal constrained control for generally damped Brownian heat engines
• Revisiting Endo-reversible Carnot engine: Extending the Yvon engine
• Chiral and non-chiral swift mode conversion near an exception point with dynamic adiabaticity engineering
• Perturbative expansion of irreversible works in symmetric and asymmetric processes
• Heat engine model exhibit super-universal feature and capture the efficiencies of different power plants
• Harvesting energy from a periodic heat bath
• Accelerating the heat diffusion: fast thermal relaxation of a microcantilever
• On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula
• Unified trade-off optimization of quantum harmonic Otto engine and refrigerator
• Optimizing low-dissipation Carnot-like thermal devices with heat leak
• Optimizing power and efficiency of a single spin heat engine
• Exploring outputs from concatenated stochastic heat engines
• Energetics and efficiency of a molecular motor model
• Machines of life: catalogue, stochastic process modeling, probabilistic reverse engineering and the PIs- from Aristotle to Alberts
• Universal bounds on fluctuations for machines with broken time-reversal symmetry
• Lower Bound of Entropy Production in an Underdamped Langevin System with Normal Distributions
• Steady-state heat engines driven by finite reservoirs
• Second moments of work and heat for a single particle stochastic heat engine in a breathing harmonic potential
• Optimal power and efficiency of odd engines