R. Hurtado-Gutiérrez, P.I. Hurtado, C. Pérez-Espigares
Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. One of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While the Macroscopic Fluctuation Theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete ℤn symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. We show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate manifold. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in three paradigmatic many-body systems: (i) the 1D boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (ii) the 3 and 4-state Potts model, which displays discrete rotational symmetry-breaking DPT for energy fluctuations, and (iii) the closed WASEP which presents a continuous symmetry-breaking DPT to a time-crystal phase characterized by a rotating condensate.
R. Hurtado-Gutiérrez, F. Carollo, C. Pérez-Espigares, P. I. Hurtado
Symmetry-breaking dynamical phase transitions (DPTs) abound in the fluctuations of nonequilibrium systems. Here we show that the spectral features of a particular class of DPTs exhibit the fingerprints of the recently discovered time-crystal phase of matter. Using Doob’s transform as a tool, we provide a mechanism to build classical time-crystal generators from the rare event statistics of some driven diffusive systems. An analysis of the Doob’s smart field in terms of the order parameter of the transition then leads to the time-crystal lattice gas (tcLG), a model of driven fluid subject to an external packing field which presents a clear-cut steady-state phase transition to a time-crystalline phase characterized by a matter density wave which breaks continuous time-translation symmetry and displays rigidity and long-range spatio-temporal order, as required for a time crystal. A hydrodynamic analysis of the tcLG transition uncovers striking similarities, but also key differences, with the Kuramoto synchronization transition. Possible experimental realizations of the tcLG in colloidal fluids are also discussed.
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence. However, during the last decade advanced computational techniques have been developed to measure rare events in simulations of many-particle systems that allow for the first time the direct observation and characterization of these DPTs. Here we review the application of a particular rare-event simulation technique, based on cloning Monte Carlo methods, to characterize DPTs in paradigmatic stochastic lattice gases. In particular, we describe in detail some tricks and tips of the trade, paying special attention to the measurement of order parameters capturing the physics of the different DPTs, as well as to the finite-size effects (both in the system size and number of clones) that affect the measurements. Overall, we provide a consistent picture of the phenomenology associated with DPTs and their measurement.
Using tools from large deviation theory, we study fluctuations of the heat current in a model of d-dimensional incompressible fluid driven out of equilibrium by a temperature gradient. We find that the most probable temperature fields sustaining atypical values of the global current can be naturally classified in an infinite set of curves, allowing us to exhaustively analyze their topological properties and to define universal profiles onto which all optimal fields collapse. We also compute the statistics of empirical heat current, where we find remarkable logarithmic tails for large current fluctuations orthogonal to the thermal gradient. Finally, we determine explicitly a number of cumulants of the current distribution, finding remarkable relations between them.
P.L. Garrido, P.I. Hurtado, D. Manzano, F. de los Santos
The special issue of European Physical Journal Special Topics has been finally published. It originated at the 14th Granada Seminar on Quantum Systems in and out of equilibrium: Fundamentals, dynamics and applications, which took place in 2017, from June 20 to June 23 in Granada, Spain. This edition was sponsored by the University of Granada through the Department of Electromagnetism and Physics of the Matter and the Faculty of Sciences, the Spanish Minister of Economy, Industry and Competitiveness, and the European Physical Society. There were in this edition a total of 57 lectures and 27 poster contributions covering quantum aspects of thermalization, quantum transport, quantum effects in condensed matter, biology, quantum computation, open quantum systems, quantum fluctuations and large deviations, and quantum thermodynamics.
C. Pérez-Espigares, F. Carollo, J.P. Garrahan, P.I. Hurtado
Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a ℤ2 symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations of the microscopic dynamics.
Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on this problem, shedding light on e.g. the reasons behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions and new symmetries. This makes the understanding of the properties of these optimal paths a central issue. Here we derive a fundamental relation which strongly constraints the architecture of these optimal paths for general d-dimensional nonequilibrium diffusive systems, and implies a non-trivial structure for the dominant current vector fields. Interestingly, this general relation (which encompasses and explains previous results) makes manifest the spatio-temporal non-locality of the current statistics and the associated optimal trajectories.
N. Tizón-Escamilla, C. Pérez-Espigares, P.L. Garrido, P.I. Hurtado
Dynamic phase transitions (DPTs) at the fluctuating level 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 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 currents in 2d leads to a rich phase diagram, with different symmetry-broken fluctuation phases separated by lines of 1st– and 2nd-order DPTs. Order in the form of coherent jammed states emerges to hinder transport for low-current fluctuations, revealing a deep connection between rare events and self-organized structures which enhance their probability, an observation of broad implications.
Carlos Pérez-Espigares, Pedro L. Garrido, Pablo I. Hurtado
The additivity principle (AP) allows to compute the current distribution in many one-dimensional (1d) nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d=2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d>1. We prove that, when compared to the straightforward extension of the AP to high-d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the non-equilibrium behaviour of the system of interest; their statistics, associated structures and microscopic origin. During the last years, some new general and powerful methods have appeared to delve into fluctuating behaviour that have drastically changed the way to address this problem in the realm of diffusive systems: macroscopic fluctuation theory (MFT) and a set of advanced computational techniques that make it possible to measure the probability of rare events. Notwithstanding, a satisfactory theory is still lacking in a particular case of intrinsically non-equilibrium systems, namely those in which energy is not conserved but dissipated continuously in the bulk of the system (e.g. granular media). In this work, we put forward the dissipated energy as a relevant quantity in this case and analyse in a pedagogical way its fluctuations, by making use of a suitable generalisation of macroscopic fluctuation theory to driven dissipative media.