Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat-engine model

Abstract

We investigate the stochastic thermodynamics of a two-particle Langevin system. Each particle is in contact with a heat bath at different temperatures T_{1} and T_{2} (<T_{1}), respectively. Particles are trapped by a harmonic potential and driven by a linear external force. The system can act as an autonomous heat engine performing work against the external driving force. Linearity of the system enables us to examine thermodynamic properties of the engine analytically. We find that the efficiency of the engine at maximum power η_{MP} is given by η_{MP}=1-sqrt[T_{2}/T_{1}]. This universal form has been known as a characteristic of endoreversible heat engines. Our result extends the universal behavior of η_{MP} to nonendoreversible engines. We also obtain the large deviation function of the probability distribution for the stochastic efficiency in the overdamped limit. The large deviation function takes the minimum value at macroscopic efficiency η=η[over ¯] and increases monotonically until it reaches plateaus when η≤η_{L} and η≥η_{R} with model-dependent parameters η_{R} and η_{L}.

Stochastic efficiency of an isothermal work-to-work converter engine

“…While the first two features were not introduced in this context earlier as reported in Refs. [51,55], the third feature is similar to as mentioned in Ref. [55].…”

“…1(b)], the contribution to P t (W 1 ,W 2 ) comes from both saddle and branch points as given by Eq. (55). Thus, for the region where g(λ 1 , λ 2 ) does not have any singularity (see Fig.…”

“…1(b)], we need to be careful while computing the asymptotic form of P t (W 1 ,W 2 ), as given by Eq. (55).…”

“…Moreover, the probability density function for stochastic efficiency is also computed, and all of these results were verified experimentally by them. Park et al [55] modeled an engine which is driven by time-independent (time-symmetric) driving. In contrast to Refs.…”

Brownian Duet: A Novel Tale of Thermodynamic Efficiency

“…However, nonisothermal conditions are not natural in the Brownian world-in the Stirling-engine experiment, heating requires a strong laser pulse-nor, in fact, in most of the biological world. Furthermore, applying stochastic thermodynamics to a heat-to-work transformation is more involved because of the non-Gaussian distribution of heat fluctuations [65][66][67][68], rendering the theoretical analysis and interpretation of the engine and its efficiency much more complicated [69].…”