Maximal power output of a stochastic thermodynamic engine

Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines, by bounding the maximal amount of mechanical energy produced, compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasistatic processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Indeed, the problem to optimize power can be expressed as a stochastic control problem. Building on this framework of stochastic thermodynamics we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (T-c cold, and T-h hot). Specifically, assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by M8 (T-h/T-c - 1). Moreover, we show that this bound can be reached to within a factor of (T-h/T-c - 1)/( T-h/T-c + 1) by operating the cyclic thermodynamic process with a quadratic potential. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

Classical thermodynamics focuses on quantifying the efficiency of thermodynamic engines and the challenge lies in estimating the upper limit of power transmission. Recent insights from stochastic models provide a new perspective for practice, indicating that power optimization can be achieved through stochastic control. By utilizing the framework of stochastic thermodynamics, bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential can be derived.