Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator

Abstract

We analyse non-equilibrium Carnot-like cycles built with a colloidal particle in a harmonic trap, which is immersed in a fluid that acts as a heat bath. Our analysis is carried out in the overdamped regime. The cycle comprises four branches: two isothermal processes and two locally adiabatic ones. In the latter, both the temperature of the bath and the stiffness of the harmonic trap vary in time, but in such a way that the average heat vanishes for all times. All branches are swept at a finite rate and, therefore, the corresponding processes are irreversible, not quasi-static. Specifically, we are interested in optimising the heat engine to deliver the maximum power and characterising the corresponding values of the physical parameters. The efficiency at maximum power is shown to be very close to the Curzon-Ahlborn bound over the whole range of the ratio of temperatures of the two thermal baths, pointing to the near optimality of the proposed protocol.

Compatibility of Carnot efficiency with finite power in an underdamped Brownian Carnot cycle in small temperature-difference regime

“…Although we have used the instantaneous adiabatic process, the other type of adiabatic process can be used for the study of the Brownian Carnot cycle [24,28,35,36]. In this adiabatic process, the system contacts with a heat bath with varying temperature that maintains vanishing heat flow between the system and the heat bath on average.…”

Correlation-enhanced Stability of Microscopic Cyclic Heat Engines

“…In the past three decades, stochastic thermodynamics has been developed to formulate laws of thermodynamics for fluctuating thermodynamic quantities of small systems, and has made a great success in understanding of thermodynamics of small systems [13][14][15][16]. Motivated by the experimental realization of microscopic heat engines and the theoretical advances in thermodynamics of small systems, there is a surge of activity on the study of microscopic heat engines [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Recently, fluctuations of the performance of microscopic heat engines and characterization of their performance beyond the mean values of thermodynamic quantities starts to be an active research topic [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

“…This kind of time optimisation problem is important from a fundamental point of view and also has relevance for applications. For the connection between equilibrium states, related problems emerge in the optimisation of irreversible heat engines [ 46 ], the analysis of the Mpemba effect [ 21 , 47 , 48 , 49 ], and the optimisation of the relaxation route to equilibrium [ 50 , 51 , 52 ].…”