Fast forward approach to stochastic heat engine

Abstract

The fast-forward (FF) scheme proposed by Masuda and Nakamura (\textit{Proc. R. Soc. A} \textbf{466}, 1135 (2010)) in the context of conservative quantum dynamics can reproduce a quasi-static dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high ($T_h$)- and low ($T_c$)-temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally-adiabatic processes, and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency $\eta$ at the maximum power of this engine is found to be ${\eta }^{\ast }=\frac{1}{2}\left(1+\frac{1}{2}{\left(\frac{T_c}{T_h}\right)}^{\frac{1}{2}}-\frac{5}{4}\frac{T_c}{T_h}+O\left({\left(\frac{T_c}{T_h}\right)}^{\frac{3}{2}}\right)\right)$ and ${\eta }^{\ast }=1-{\left(\frac{T_c}{T_h}\right)}^{\frac{1}{2}}$, respectively in the cases of strong and weak dissipation. The result is justified for a wide family of time scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.

arXiv comment14 pages, 3 figures

References in corpus (21)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Fast optimal frictionless atom cooling in harmonic traps
• Shortcuts to adiabaticity
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Efficiency at maximum power of low dissipation Carnot engines
• Brownian Carnot engine
• Fast-forward of adiabatic dynamics in quantum mechanics
• Engineered swift equilibration of a Brownian particle
• Efficiency at maximum power of minimally nonlinear irreversible heat engines
• An all-optical nanomechanical heat engine
• Adiabatic processes realized with a trapped Brownian particle
• Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity
• Shortcuts to isothermality and nonequilibrium work relations
• The Carnot Cycle for Small Systems: Irreversibility and the Cost of Operations
• Underdamped stochastic heat engine at maximum efficiency
• Entropy production for mechanically or chemically driven biomolecules
• Fast forward to the classical adiabatic invariant
• Entropic anomaly and maximal efficiency of microscopic heat engines
• Fast-forward approach to adiabatic quantum dynamics of regular spin clusters: nature of geometry-dependent driving interactions
• Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of states

Cited by in corpus (19)

• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Geodesic path for the minimal energy cost in shortcuts to isothermality
• Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator
• Abstract models for heat engines
• A microscopic theory of Curzon-Ahlborn heat engine
• Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols
• Thermal brachistochrone for harmonically confined Brownian particles
• Optimal time-entropy bounds and speed limits for Brownian thermal shortcuts
• Optimizing Brownian heat engine with shortcut strategy
• Equilibrium free energy differences from a linear nonequilibrium equality
• Microscopic low-dissipation heat engine via shortcuts to adiabaticity and shortcuts to isothermality
• Fast-forward scaling theory
• Fast forward evolution in heat equation:Tunable heat transport in adiabatic regime
• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality
• Active charge and discharge of a capacitor: scaling solution and energy optimization
• Maximum power Stirling-like heat engine with a harmonically confined Brownian particle
• Time-Optimal Transport of a Harmonic Oscillator: Analytic Solution
• Fast-forward scaling theory for quantum dynamics on curved space-time