1 research outputs found
Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions
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.Comment: 21 pages, 7 figure