Optimal finite-time Brownian Carnot engine

Abstract

Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional "textbook" engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finitetime, nonequilibrium cyclic operation of the parametric harmonic oscillator contact with with a time-varying heat bath, with particular focus on the Brownian Carnot cycle. We derive the optimally parametrized Carnot cycle, along with two other new cycles and compare their dissipated energy, efficiency, and steady-state power production against each other and a previously tested experimental protocol for the Carnot cycle. We demonstrate a 20% improvement in dissipated energy over previous experimentally tested protocols and a ∼50% improvement under other conditions for one of our engines, while our final engine is more efficient and powerful than the others we considered. Our results provide the means for experimentally realizing optimal mesoscale heat engines.

Relation between fluctuations and efficiency at maximum power for small heat engines

“…(2) MP and minimizing the fluctuation of work output for the finite-time heat engines are interesting open problems. Also, thermodynamic geometry [25,26,58,[75][76][77][78] is a good method leads to further studies on the properties of η (2) .…”

Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

“…This has enabled finding optimal driving protocols in such regime for complex systems such as a two dimensional Ising model [33,34], nanomagnets [35], and quantum spin chains [36]. Optimal protocols for different classes of slowly driven heat engines have also been developed by such a geometric approach [32,[37][38][39][40][41][42][43][44]. Besides the slow driving regime, the optimization problem can also be simplified in the opposite, fast-driving, regime [45][46][47][48].…”

Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines

“…Interestingly, such a geometric description is also possible for its fluctuation. We apply our framework to the current experiment and provide an optimum scheme to reduce both the mean and the fluctuation of the dissipation (see also [72] for optimization of the mean value).…”