Spontaneous Symmetry Breaking at the Fluctuating Level

Abstract

Phase transitions not allowed in equilibrium steady states may happen, however, at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.

Renormalized time scale for anticipating and lagging synchronization

“…(5.7) and the associated discussion, ν decreases as ν grows so larger system sizes are needed to observe convergence to the macroscopic limit. In addition, finite-size effects related to the number of clones M used for the sampling become an issue in this limit [13,31]. In any case, the sharpening of G(d) as ν increases for any β shows that large dissipation fluctuations are strongly suppressed in this regime, as was argued for ν 1 on quite general grounds in Sec.…”

“…In conservative systems, this conjecture has been shown [7] to be equivalent to the additivity principle recently introduced to study current fluctuations in diffusive media [8]. The validity of this additivity scenario has been recently confirmed in extensive numerical simulations for a broad interval of fluctuations [11,14], though it may eventually break down for extreme fluctuations via a dynamic phase transition [30,31]. As we will see below, the applicability of this generalization of the additivity conjecture to dissipative systems is well supported by numerical evidence.…”

“…This opens the door to further general results in the nonequilibrium statistical physics of dissipative media. In particular, it would be interesting to explore the existence of phase transitions and spontaneous symmetry breaking at the fluctuating level therein, in a way similar to the phenomenon reported in conservative systems [30,31]. Moreover, as the relevant magnitudes characterizing nonequilibrium behavior in dissipative systems are both the dissipated energy and the current, it would be worth analyzing the joint fluctuations of these two observables within the MFT approach.…”

Dynamic phase transitions in simple driven kinetic networks

“…1). While this Markovian system, with effectively one-particle dynamics, lacks much of the complexity of previously studied driven systems [4][5][6][7][8], we show -numerically and analyticallythe presence of two dynamical phases, each with a characteristic entropy production rate. This demonstration shows that singularities in trajectory space can in fact arise even in very simple driven kinetic networks with a single degree of freedom.…”

“…Analysis of fluctuations in non-equilibrium processes have, for example, led to the discovery of the fluctuation theorems, which have helped elucidate how macroscopic notions of irreversibility emerge from microscopic laws [1][2][3]. More recently, theoretical and numerical analysis of the statistics of rare fluctuations in driven lattice gas models [4,5], exclusion processes [6], zero-range processes [7], 1D models of transport [8], and models of glass formers [9,10] have revealed the presence of coexisting ensembles of trajectories and so-called dynamic phase transitions between them [4,5,8,11]. In this paper, we analyze the statistics of rare fluctuations in entropy production rates for certain model non-equilibrium, or driven, kinetic networks (see Fig.…”