Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state

Abstract

Long-ranged correlations generically exist in non-equilibrium fluid systems. In the case of a nonequilibrium steady state caused by a temperature gradient the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently the Casimir force or pressure due to these fluctuations or correlations have been discussed in great detail. In this paper the notion of a Casimir work is introduced and a novel way to measure the non-equilibrium Casimir force is suggested. In particular, the non-equilibrium Casimir force is related to a non-equilibrium heat and not, as in equilibrium, to a volume derivative of an average energy. The non-equilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The non-equilibrium work distribution is also computed, and contrasted to work distributions in systems with shortrange correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in non-equilibrium steady states are not explicit enough to illustrate any of these interesting features.

Quantum work fluctuations in connection with the Jarzynski equality

“…In both classical and quantum cases, the ensemble average of a highly nonlinear (in fact, exponential) function of work, as requested by JE, could become practically demanding in yielding a wellconverged result for ∆F, as rare events can potentially dominate the average [3,19]. This in fact has motivated a number * phygj@nus.edu.sg of studies in the literature to investigate the errors in predicting ∆F based on JE [20][21][22][23][24][25][26][27]. As suggested by the central limit theorem (CLT), the errors are related to the variance in the exponential work, i.e., var(e −βW ) ≡ e −2βW − e −2β ∆F .…”

Work fluctuation theorems and free energy from kinetic theory

“…The order of magnitude of the number of trajectories required to obtain a result with low noise level is very high, at least several thousands in the simulations we have performed (DSMC and MD). This difficulty has already been pointed out in the literature [25,26,27]. Consequently, it is hard to see any advantage of this procedure over measuring the work in the quasistatic limit of an isothermal process, in order to measure equilibrium free energy changes.…”

Contrasting Work Fluctuations and Distributions in Systems with Short-Range and Long-Range Correlations

“…Here c p , γ, α are, respectively, the specific heat capacity at constant pressure, the ratio of specific heat capacities, and the coefficient of thermal expansion. The fluctuating work in this case is given by d W NE = − p NE (L)dV where p NE (L) is the spatial average of p NE (x) [20][21][22]. If the system expands in the z-direction from length L to length L(1 + ∆), and if |∆| ≪ 1, then the fluctuating non-equilibrium work is simply…”

“…[32] The result given for this quantity in [20] was different because the work distribution given there was exact only for the region WNE ≫ 1, and not the WNE → 0 limit, which is the important part of the distribution for determining FNE(bNEL 2 ≫ 1 (17) for the NE fluid case. As noted in Remark 3, however, in this limit Eq.…”

“…In [8] it was shown that the fluctuations in the JFT are so large for systems with short-range correlations, that they invalidate its practical use for all but the smallest systems.…”