Symmetries in fluctuations far from equilibrium

Abstract

Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. large deviations | rare events | hydrodynamics | transport | entropy production L arge fluctuations, though rare, play an important role in many fields of science as they crucially determine the fate of a system (1). Examples range from chemical reaction kinetics or the escape of metastable electrons in nanoelectronic devices to conformational changes in proteins, mutations in DNA, and nucleation events in the primordial universe. Remarkably, the statistics of these large fluctuations contains deep information on the physics of the system of interest (2, 3). This is particularly important for systems far from equilibrium, where no general theory exists up to date capable of predicting macroscopic and fluctuating behavior in terms of microscopic physics, in a way similar to equilibrium statistical physics. The consensus is that the study of fluctuations out of equilibrium may open the door to such general theory. As most nonequilibrium systems are characterized by currents of locally conserved observables, understanding current statistics in terms of microscopic dynamics has become one of the main objectives of nonequilibrium statistical physics (2-17). Pursuing this line of research is both of fundamental as well as practical importance. At the theoretical level, the function controlling current fluctuations can be identified as...

Renormalized time scale for anticipating and lagging synchronization

“…By using this fluctuating hydrodynamic picture together with a path integral formulation, we derive a general form for the action associated to a history of the density, current and dissipation fields (that is, a path in mesoscopic phase space). Remarkably, this action takes the same form as in conservative nonequilibrium systems [7][8][9][10][11][12][13][14], simplifying the analysis in the dissipative case. This is both an important and a surprising result, which stems from the quasi-elastic character of the underlying microscopic dynamics in the large system size limit.…”

“…These intriguing "symmetries" appear as a consequence of the invariance under time reversal of the underlying microscopic dynamics. These and other recent results [5][6][7][8][9][10][11][12][13][14] are however restricted to nonequilibrium "conservative" systems characterized by currents.…”

“…Therefore, the understanding of current statistics in terms of the microscopic dynamics represents one of the main problems of nonequilibrium statistical mechanics, triggering an intense research effort in recent years. In this context, key results are the Gallavotti-Cohen fluctuation theorem [5], which relates the probability of observing a given current fluctuation J with the probability of the reversed event − J, or the recently-introduced Isometric Fluctuation Relation [14], which relates the probability of any pair of isometric current fluctuations ( J, J ), with | J| = | J |. These intriguing "symmetries" appear as a consequence of the invariance under time reversal of the underlying microscopic dynamics.…”

“…A classical example is the fluctuation-dissipation theorem, which relates the linear response of a system to an external perturbation to the fluctuation properties of the system in thermal equilibrium [2,3]. More recently, the investigation of general properties of fluctuations in nonequilibrium steady states is opening new paths for understanding physics far from equilibrium [4][5][6][7][8][9][10][11][12][13][14]. The study of fluctuation statistics of macroscopic observables provides an alternative path to obtain thermodynamic potentials, a complementary approach to the usual ensemble description.…”

“…In particular, when the colliding pair is chosen completely at random, independently of the value of its energy, the Kipnis-Marchioro-Presutti (KMP) model [23] for heat conduction is recovered in the conservative case. The KMP model plays a main role in nonequilibrium statistical physics as a touchstone to test theoretical advances [5,6,8,[11][12][13][14][15]23]. Our general class of models contains the essential ingredients characterizing most dissipative media, namely: (i) diffusive dynamics, (ii) bulk dissipation, and (iii) boundary injection.…”