Category Archives: large deviations

Sampling rare events across dynamical phase transitions

C. Pérez-Espigares, P. I. Hurtado

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.

Chaos 29, 083106 (2019); arXiv:1902.01276

Infinite family of universal profiles for heat current statistics in Fourier’s law

P. L. Garrido, P. I. Hurtado, N. Tizón-Escamilla

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.

Phys. Rev. E 99, 022134 (2019); arXiv:1810.10778

Quantum systems in and out of equilibrium: Fundamentals, dynamics and applications

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.

Eur. Phys. J Special Topics 227, 201 (2018)

Dynamical criticality in driven systems: non-perturbative physics, microscopic origin and direct observation

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.

Phys. Rev. E 98, 060102(R) (2018); arXiv:1807.10235

Harnessing symmetry to control quantum transport

D. Manzano and P.I. Hurtado

Controlling transport in quantum systems holds the key to many promising quantum technologies. Here we review the power of symmetry as a resource to manipulate quantum transport, and apply these ideas to engineer novel quantum devices. Using tools from open quantum systems and large deviation theory, we show that symmetry-mediated control of transport is enabled by a pair of twin dynamic phase transitions in current statistics, accompanied by a coexistence of different transport channels. By playing with the symmetry decomposition of the initial state, one can modulate the importance of the different transport channels and hence control the flowing current. Motivated by the problem of energy harvesting we illustrate these ideas in open quantum networks, an analysis which leads to the design of a symmetry-controlled quantum thermal switch. We review an experimental setup recently proposed for symmetry-mediated quantum control in the lab based on a linear array of atom-doped optical cavities, and the possibility of using transport as a probe to uncover hidden symmetries, as recently demonstrated in molecular junctions, is also discussed. Overall, these results demonstrate the importance of symmetry not only as a organizing principle in physics but also as a tool to control quantum systems.

Adv. in Phys. 67, 1 (2018)arXiv:1707.07895

Structure of the optimal path to a fluctuation

N. Tizón-Escamilla, P.I. Hurtado and P.L. Garrido

Macroscopic fluctuations have become an essential tool to understand physics far fromfig 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.

Phys. Rev. E 95, 032119 (2017);  arXiv:1611.02500

Order and symmetry-breaking in the fluctuations of driven systems

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.

Phys. Rev. Lett. 119, 090602 (2017); arXiv:1606.07507

Weak additivity principle for current statistics in d-dimensions

Carlos Pérez-Espigares, Pedro L. Garrido, Pablo I. Hurtado

screenshot_14The 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.

Phys. Rev. E 93, 040103(R) (2016)arXiv:1511.08373

Statistics of the dissipated energy in driven diffusive systems

A. Lasanta, Pablo I. Hurtado, A. Prados

screenshot_56Understanding 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.

Eur. Phys. J. E 39, 35 (2016); arXiv:1508.07635

Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation

Pablo I. Hurtado, Carlos P. Espigares, Jesus J. del Pozo, Pedro L. Garrido

screenshot_16Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics and associated structures. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.

J. Stat. Phys. 154, 214 (2014)arXiv:1312.1246