2020/01/03 by Rui Fu, Fu, Rui, Amirhossein Taghvaei +5 · 1 citation
Chemistry · Engineering · Physics and Astronomy · #49-XX #60-XX #Advanced Thermodynamics and Statistical Mechanics #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Phase Equilibria and Thermodynamics #Systems and Control (eess.SY) #electronic engineering #information engineering #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.2001.00979
openalex publication_date 2020/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. Building on this framework of \em 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 (Tc cold, and Th 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 (M)/(8)((Th)/(Tc)-1). Moreover, we show that this bound can be reached to within a factor of ((Th)/(Tc)-1)/((Th)/(Tc)+1) by operating the cyclic thermodynamic process with a quadratic potential.