Understanding the physics of nonequilibrium systems remains as one of the major challenges of modern theoretical physics. We believe nowadays that this problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics, associated structures and microscopic origin. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new powerful and 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.

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...

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows to measure for the first time the marginal anomaly of the heat conductivity predicted for hard disks.PACS numbers: 05.70.Ln, 44.10.+i, The understanding of nonequilibrium behavior remains as one of the major challenges in theoretical physics, even in the simplest situations posed by nonequilibrium steady states (NESSs) [1][2][3][4][5][6][7][8]. The first thing one notices in typical NESSs (as those obtained for fluids under a temperature gradient) is the nontrivial, inhomogeneous structure that the system of interest develops in response to the nonequilibrium driving. This structure, readily measurable in experiments or simulations, carries information on the governing nonequilibrium macroscopic laws (e.g. Fourier's law) which emerge from the myriad of interacting microscopic constituents. It is therefore of paramount importance to understand general properties of these structures, consubstantial to nonequilibrium behavior. With this idea in mind, we derive here a set of simple yet general scaling laws for a broad class of d-dimensional fluids driven far from equilibrium by a temperature gradient. In particular, we show that the fluid's density and temperature profiles follow from two master curves, independent of the driving force and the system parameters, after a simple linear scaling of space. This strong result is based on two mild hypotheses, namely macroscopic local equilibrium and Fourier's law, together with a rather general assumption on the fluid's equation of state.We then proceed to test the emerging picture in a quintessential model, the hard disk fluid. Hard sphere (HS) models and their relatives are among the most successful, inspiring and prolific models of physics, as they contain the essential ingredients to understand a large class of complex phenomena, from phase transitions or heat transport to glassy dynamics, jamming, or the physics of liquid crystals and granular materials, to mention just a few [6,[9][10][11][12][13][14][15][16][17][18][19][20][21][22], turning general results for * jpozo@onsager.ugr.es † garrido@onsager.ugr.es ‡ phurtado@onsager.ugr.es these systems even more appealing. Extensive computer simulations of hard disks under tempe...

A Penning-trap facility for high-precision mass spectrometry based on a novel detection method has been built. This method consists in measuring motional frequencies of singly-charged ions trapped in strong magnetic fields through the fluorescence photons from laser-cooled 40 Ca + ions, to overcome limitations faced in electronic single-ion detection techniques. The key element of this facility is an open-ring Penning trap coupled upstream to a preparation Penning trap similar to those used at Radioactive Ion Beam facilities. Here we present a full characterization of the trap and demonstrate motional frequency measurements of trapped ions stored by applying external radiofrequency fields in resonance with the ions' eigenmotions, in combination with time-of-flight identification. The infrastructure developed to observe the fluorescence photons from 40 Ca + , comprising the 12 laser beams and the optical system to register the image in a high-sensitive CCD sensor, has been proved by taking images of the trapped and cooled 40 Ca + ions. This demonstrates the functionality of the proposed laser-based mass-spectrometry technique, providing a unique platform for precision experiments with implications in different fields of physics.

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