Dissipation Bounds All Steady-State Current Fluctuations

Abstract

Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linearresponse variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linearresponse-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations. DOI: 10.1103/PhysRevLett.116.120601 One of the most useful insights into thermodynamics has been that fluctuations near equilibrium are completely characterized by just one principle: the fluctuationdissipation theorem [1]. Far from equilibrium, however, fluctuations exhibit less universal structure. As such, characterizing the rich anatomy of nonequilibrium fluctuations has been handled on a case by case basis, with few universal nonequilibrium principles. Notable exceptions are the fluctuation theorems [2][3][4][5][6][7], as well as fluctuationdissipation theorems for nonequilibrium steady states [8][9][10][11][12]. Recently, Barato and Seifert have proposed a new kind of nonequilibrium principle, a thermodynamic uncertainty relation that expresses a trade-off between the variance of current fluctuations and the rate of entropy production [13]. It reveals that away from equilibrium, dissipation continues to regulate small fluctuations. While the thermodynamic uncertainty relation was not proven in general, analytical calculations and numerical evidence support its validity [13]. Applications appear myriad, and already include insights into chemical kinetics as well as biochemical sensing [14,15].In this Letter, we demonstrate that dissipation in fact constrains all current fluctuations. In particular, we prove a pair of general thermodynamic inequalities for the large deviation function of the steady-state empirical currents in Markov jump processes. Such processes model a variety of scenarios, including molecular motors [16], chemical reaction networks [17,18], and mesoscopic quantum devices [19]. Our analysis reveals that far from equilibrium, current fluctuations are always more probable than would be predicted by linear response [20,21]. Remarkably, our relationship bounds even rare fluctuations (large deviations), and by specializing to small deviations we obtain the thermodynamic uncertainty relation.We have in mind a system with N mesoscopic states (or configurations), x ¼ 1; …; N. Transitions between pairs of states, say from y to z, are modeled as a continuous-time Markov jump process with rates rðy; zÞ [22]. It is convenient to picture these dynamics occurring on a graph (as in Fig. 1), with vertices denoting states and edges (or links) symbolizing possible transitions. We assume the dynamics to be ergodic and that rðz; yÞ > 0 whenever rðy; zÞ > 0, so ...

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

“…While the thermodynamic uncertainty relation has originally recognized the bound of steady-state current fluctuation ( J ) [12], here we show that the relation of variance of heat dissipation with its mean (Eq.21) can be deduced from it as well.…”

“…This effort has recently been followed by a general proof employing the large deviation theory [12][13][14]. * hyeoncb@kias.re.kr…”

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

“…The first are general bounds on the fluctuations of time-integrated currents [1][2][3][4]. Obtained by means Level 2.5 [5][6][7] dynamical large deviation methods [8][9][10][11][12], these results stipulate general lower bounds for fluctuations at any order of all empirical currents in the stationary state of a stochastic process [1][2][3][4].…”

“…[2] (called "exponential bound"); here we rederive it straightforwardly via Level 2.5 large deviations; cf. [1]. In Sec.…”

“…[1][2][3][4] and [13][14][15][16][17][18] focus on trajectory observables asymmetric under time reversal, such as empirical currents, which can be positive or negative and can increase and decrease with time. Here we consider instead trajectory observables which are always non-negative and strictly nondecreasing with time.…”