Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions

Abstract

We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven with a constant rate. The time evolution of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the performed work during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility.

Stochastic thermodynamics under coarse graining

“…They coincided with an unprecedented development in the experimental techniques used to manipulate small systems and triggered a great deal of experimental studies in a variety of contexts, such as single molecule stretching experiments [35,[38][39][40], nanomechanical oscillator work measurements [41], spectroscopic measurement of trajectory entropies [42,43], and electronic current fluctuations in full counting statistics experiments [44]. Since stochastic thermodynamics combines kinetics and thermodynamics, it has also proved extremely useful to describe the finite-time thermodynamics (e.g., efficiency at finite power) of various nanodevices operating as thermodynamic machines [45][46][47][48][49][50][51][52][53][54]. Overall, this theory is becoming a fundamental tool for the study of nanosciences.…”

Large fluctuations of radiation in stochastically activated two-level systems

“…Measurements of the dissipated work [20] and entropy [23] agree with the expected integral fluctuation relations. Fluctuation relations for driven two-level systems have been investigated recently also in the context of biological motors [6] and quantum two-level systems [16].…”

Work and power fluctuations in a critical heat engine

“…is fulfilled. In this special case f w ∝ 1 and thus one obtains in the large system limit finite, but nonzero work fluctuations which are normally observed for microscopic heat engines only [15][16][17][18][19][20][21][22][23][24][25].…”