Entropy production in the nonequilibrium steady states of interacting many-body systems

Abstract

Entropy production is one of the most important characteristics of non-equilibrium steady states.We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of non-equilibrium systems: transport systems and reaction-diffusion systems. The usefulness of the mean entropy production rate and of the large deviation function of the entropy production for characterizing non-equilibrium steady states of interacting manybody systems is discussed. We show that the large deviation function displays a kink-like feature at zero entropy production that is similar to that observed for a single particle driven along a periodic potential. This kink is a direct consequence of the detailed fluctuation theorem fulfilled by the probability distribution of the entropy production and is therefore a generic feature of the corresponding large deviation function.

Current fluctuations in a particle-nonconserving reaction-diffusion process

“…2(a). As q → 1 the system approaches to its equilibrium state, hence e s (µ) is almost parabolic [24,25]. It can be seen that e s (µ) behaves almost the same way for large values of q.…”

“…2(c) the first derivative of large deviation function for the entropy production rate respect to σ for q = 2 and two values of γ, one above and one below the transition point, is plotted. Using (14) one can easily find that [24]…”

Entropy production and large deviation function for systems with microscopically irreversible transitions

“…The symmetry property of the LDF, I(σ) − I(−σ) = − Ṡ m σ, implies that the fluctuation relation for the entropy production in the medium holds for the system in the long time limit. The plot of the LDF for the entropy production (see figure 6(a)) shows a kink at zero entropy production as a consequence of the fluctuation theorem [17,20]. The distribution function for the entropy production, as shown in 6(b), is obtained directly from equation (47).…”

“…For a system described by the continuous time Markov dynamics, a microscopic transition from its configuration i to j with a transition rate, ω ij , causes the entropy of the surrounding medium to change [5,6,[9][10][11][12] by the amount ∆S m = ln ωij ωji , where k B , the Boltzmann constant, is assumed to be unity. Of the many studies on the entropy production of the medium for systems with microscopic reversibility [11,12,[14][15][16][17], some recent works on the properties of the LDF and its symmetry relation can be found in [16,17] where the authors studied the asymptotic distributions of the entropy production by finding out the LDF using a generating function based approach. In reference [17], the authors obtained the LDF for partially asymmetric simple exclusion processes and reaction-diffusion processes with microscopic reversibility.…”

“…These new rates are used to obtain the average rate of medium entropy production and further to obtain the LDF for the entropy production through a saddle point approximation. At zero entropy production, the LDFs for both the models show a kink which can be characterized by the average entropy production rate [17,20,22,23]. Finally, the LDF is used to find the distribution of the entropy production in the long time limit.…”