Stochastic efficiency: five case studies

Abstract

Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermochemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic efficiency, including the maximum of the large deviation function at the reversible efficiency, are reproduced. The approach to and extrapolation into the asymptotic time regime are documented.

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

“…Some of these models are briefly discussed in Ref. [50]. In the case of isothermal energy transformation [51], authors considered a Brownian particle in a harmonic potential driven by a duo of time-periodic forces.…”

Brownian Duet: A Novel Tale of Thermodynamic Efficiency

“…Its probability distribution, being the ratio of correlated Gaussian random variables, is given by [24,28,50]…”

“…(31), one factor _ Z by its expression from the equation of motion Eq. (28). Noting that the integral over one period of Z _ Z is zero and replacing the second factor _ Z by using Eq.…”

“…From these three distributions, we can calculate the large deviation function via the extrapolation procedure described in Appendix A of Ref. [28]. For the experimental analysis, we use the same data, which include 78000 cycles, for the different distributions, by just looking at the different cycles separately or by measuring the efficiency over multiple cycles.…”

“…The most striking result is that the second law-the positivity of entropy production-is replaced by a symmetry property for the probability distribution of this quantity, which reproduces the positivity for the average as a subsidiary consequence. The implications on the fluctuating efficiency of a small-scale engine were elucidated more recently [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. One surprising conclusion is that the maximum efficiency, corresponding to a reversible operation, can occur by chance but is, for a time-symmetric operation, exponentially less likely than any other finite efficiency.…”