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Register a new userSurvival and extreme statistics of work in steady-state heat engines
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Added by
Gonzalo Manzano Paule
Publication date
2021
fields
Physics
and research's language is
English
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We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines. We also find estimates for the time-dependent thresholds that the stochastic work does not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results, which entail an extension of martingale theory for entropy production, are tested with numerical simulations of a stochastic photoelectic device.
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We consider the quality factor Q, which quantifies the trade-off between power, efficiency, and fluctuations in steady-state heat engines modeled by dynamical systems. We show that the nonlinear scattering theory, both in classical and quantum mechanics, sets the bound Q=3/8 when approaching the Carnot efficiency. On the other hand, interacting, nonintegrable and momentum-conserving systems can achieve the value Q=1/2, which is the universal upper bound in linear response. This result shows that interactions are necessary to achieve the optimal performance of a steady-state heat engine.
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the `sampling interval used in the measurement for both `steady-state and `finite initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A `deterministic approximation is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.
The aim of this paper is to determine lost works in a molecular engine and compare results with macro (classical) heat engines. Firstly, irreversible thermodynamics are reviewed for macro and molecular cycles. Secondly, irreversible thermodynamics approaches are applied for a quantum heat engine with -1/2 spin system. Finally, lost works are determined for considered system and results show that macro and molecular heat engines obey same limitations. Moreover, a quantum thermodynamic approach is suggested in order to explain the results previously obtained from an atomic viewpoint.
Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.
In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without ..... (SEE THE PDF FOR THE REST OF THIS ABSTRACT)
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