Order and Symmetry Breaking in the Fluctuations of Driven Systems

Abstract

Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time a DPT in the current vector statistics of an archetypal two-dimensional (2d) driven diffusive system, and characterize its properties using macroscopic fluctuation theory. The complex interplay among the external field, anisotropy and vector currents in 2d leads to a rich phase diagram, with different symmetry-broken fluctuation phases separated by lines of 1 st -and 2 nd -order DPTs. Remarkably, different types of 1d order in the form of jammed density waves emerge to hinder transport for low-current fluctuations, revealing a connection between rare events and self-organized structures which enhance their probability.Introduction-The theory of critical phenomena is a cornerstone of modern theoretical physics [1, 2]. Indeed, phase transitions of all sorts appear ubiquitously in most domains of physics, from cosmological scales to the quantum world of elementary particles. In a typical 2 nd -order phase transition order emerges continuously at some critical point, as captured by an order parameter, signaling the spontaneous breaking of a symmetry and an associated non-analyticity of the relevant thermodynamic potential. Conversely, 1 st -order transitions are characterized by an abrupt jump in the order parameter and a coexistente of different phases [1, 2]. In recent years these ideas have been extended to the realm of fluctuations, where dynamical phase transitions (i.e. in the space of trajectories) have been identified in different systems, both classical [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and quantum [18][19][20][21]. Important examples include glass formers [22][23][24][25][26][27][28][29], micromasers and superconducting transistors [30,31], or applications such as DPT-based quantum thermal switches [32][33][34].DPTs appear when conditioning a system to have a fixed value of some time-integrated observable, as e.g. the current or the activity. The different dynamical phases correspond to different types of trajectories adopted by the system to sustain atypical values of this observable. Interestingly, some dynamical phases may display emergent order and collective rearrangements in their trajectories, including symmetry-breaking phenomena [5,[9][10][11], while the large deviation functions (LDFs) [35] controlling the statistics of these fluctuations exhibit nonanalyticities and Lee-Yang singularities [36][37][38][39][40][41][42][43] at the DPT reminiscent of standard critical behavior. This is a finding of crucial importance in nonequilibrium physics, as these LDFs play a role akin to the equilibrium thermodynamic potentials for nonequilibrium systems, where no bottom-up approach exists yet connecting microscopic dynamics with macroscopic properties [3, 4,44]. Moreover, the emergence of coherent structures associated * phurtado@onsager.ugr.es to rare f...

Fluctuations in Ballistic Transport from Euler Hydrodynamics

“…Seeing the SCGF as a function of the state's parameters (or of the bias), this may be interpreted as a "dynamical phase transition," of the type seen in other contexts, see e.g. [52,53,54,55,56,57,58,59,60]. We explain why this occurs from hydrodynamic principles, and how this may connect with the breaking of Gaussianity found in nonlinear fluctuating hydrodynamics [61,47,62].…”

Dynamical phase transition in drifted Brownian motion

“…The motivation for studying this model is that it shows a dynamical phase transition (DPT), that is, a sudden change in the way that fluctuations are created in the long-time limit, leading to singularities in large deviation functions, the nonequilibrium analogs of thermodynamic potentials [2]. Similar DPTs are found in interacting particle systems such as kinetically constrained models of glasses [3][4][5] and the exclusion process [6][7][8][9][10], which show DPTs in the integrated activity or current for some parameter values. In these and many other models, however, a DPT arises when taking the long-time limit in addition to a hydrodynamic or macroscopic limit [11][12][13][14], which is equivalent to a low-noise limit [15][16][17].…”

Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics

“…This system has been considered recently [37], where it was found that its large deviation function for current fluctuations in the direction of the driving exhibits a dynamical phase transition. For small λ, the system is in a homogeneous phase, while for large negative λ, the system phase separates, forming a traveling wave in the direction of the biased current.…”