Stochastic thermodynamics of self-oscillations: the electron shuttle

Abstract

Self-oscillation is a phenomenon studied across many scientific disciplines, including the engineering of efficient heat engines and electric generators. We investigate the single electron shuttle, a model nano-scale system that exhibits a spontaneous transition towards self-oscillation, from a thermodynamic perspective. We analyze the model at three different levels of description: The fully stochastic level based on Fokker-Planck and Langevin equations, the mean-field level, and a perturbative solution to the Fokker-Planck equation that works particularly well for small oscillation amplitudes. We provide consistent derivations of the laws of thermodynamics for this model system at each of these levels. At the mean-field level, an abrupt transition to self-oscillation arises from a Hopf bifurcation of the deterministic equations of motion. At the stochastic level, this transition is smeared out by noise, but vestiges of the bifurcation remain visible in the stationary probability density. At all levels of description, the transition towards self-oscillation is reflected in thermodynamic quantities such as heat flow, work and entropy production rate. Our analysis provides a comprehensive picture of a nano-scale self-oscillating system, with stochastic and deterministic models linked by a unifying thermodynamic perspective.

References in corpus (17)

• Molecular Transport Junctions: Vibrational Effects
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Thermoelectric energy harvesting with quantum dots
• Optimal energy quanta to current conversion
• Thermodynamics of a physical model implementing a Maxwell demon
• Single mode heat rectifier: Controlling energy flow between electronic conductors
• Resonant electron heating and molecular phonon cooling in single C${}_{60}$ junctions
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Shot Noise of a Quantum Shuttle
• Cooling mechanisms in molecular conduction junctions
• Single-electron Tunneling with Strong Mechanical Feedback
• Single Particle Stochastic Heat Engine
• Exactly solvable model of stochastic heat engine: Optimization of power, its fluctuations and efficiency
• Josephson Quantum Heat Engine
• Experimental realization of a Coulomb blockade refrigerator
• Dynamics of a nano-scale rotor driven by single-electron tunneling

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