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We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range of dynamical phase transitions, including spontaneous symmetry breaking into ordered states. For weak bias, the phase behaviour is controlled by extrema of the free energy, which may be local minima or saddle points. For large bias, the system tends to states of extremal activity, which may differ strongly from free energy minima. We discuss connections of these results to random first-order transition theory of glasses, which motivates an extension of the analysis to random-field Ising models where the dynamical activity is not symmetric under magnetisation reversal., 26 pages, 10 figures

We consider large deviations of the dynamical activity -- defined as the total number of configuration changes within a time interval -- for mean-field and one-dimensional Ising models, in the presence of a magnetic field. We identify several dynamical phase transitions that appear as singularities in the scaled cumulant generating function of the activity. In particular, we find low-activity ferromagnetic states and a novel high-activity phase, with associated first- and second-order phase transitions. The high-activity phase has a negative susceptibility to the magnetic field. In the mean-field case, we analyse the dynamical phase coexistence that occurs on first-order transition lines, including the optimal-control forces that reproduce the relevant large deviations. In the one-dimensional model, we use exact diagonalisation and cloning methods to perform finite-size scaling of the first-order phase transition at non-zero magnetic field., Comment: 34 pages, 11 figures, 1 table

We introduce a nonequilibrium grand-canonical ensemble defined by considering the stationary state of a driven system of particles put in contact with a nonequilibrium particle reservoir. At odds with its equilibrium counterpart, or with purely formal constructions of a grand-canonical ensemble, this physically-motivated construction yields a grand-canonical distribution that depends on the details of the contact dynamics between the system and the reservoir. For non-interacting driven particles, a grand-canonical chemical potential can still be defined, although this chemical potential now differs from that of the reservoir. However, in the general case, the usual exponential factor (in the particle number) defining the grand-canonical chemical potential, is replaced by the exponential of a non-linear function of the density, this function being proportional to the volume. This case is illustrated explicitly on a one-dimensional lattice model. Although a grand-canonical chemical potential can no longer be defined in this case, it is possible for a subclass of contact dynamics to generalize the equilibrium fluctuation-response relation by introducing a small external potential difference between the system and the reservoir., Comment: 8 pages

We investigate the non-equilibrium large deviations function of the particle densities in two steady-state driven systems exchanging particles at a vanishing rate. We first derive through a systematic multi-scale analysis the coarse-grained master equation satisfied by the distribution of the numbers of particles in each system. Assuming that this distribution takes for large systems a large deviations form, we obtain the equation (similar to a Hamilton-Jacobi equation) satisfied by the large deviations function of the densities. Depending on the systems considered, this equation may satisfy or not the macroscopic detailed balance property, i.e., a time-reversibility property at large deviations level. In the absence of macroscopic detailed balance, the large deviations function can be determined as an expansion close to a solution satisfying macroscopic detailed balance. In this case, the large deviations function is generically non-additive, i.e., it cannot be split as two separate contributions from each system. In addition, the large deviations function can be interpreted as a non-equilibrium free energy, as it satisfies a generalization of the second law of thermodynamics, in the spirit of the Hatano-Sasa relation. Some of the results are illustrated on an exactly solvable driven lattice gas model., Comment: 31 pages, 1 figure

We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviations function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factorization property. However, the nonequilibrium chemical potentials of the systems in contact keep track of the contact dynamics, and thus do not obey an equation of state. These nonequilibrium chemical potentials can be related either to the equilibrium chemical potential, or to the nonequilibrium chemical potential of the isolated systems. Results are applied both to an exactly solvable driven lattice gas model, and to the Katz-Lebowitz-Spohn model using a numerical procedure to evaluate the chemical potential., 24 pages, 6 figures

We discuss the notion of nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the non-equilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system ---which agrees with a recently proposed general definition of the chemical potential in non-equilibrium systems in contact--- we generically find that the chemical potential lacks an equation of state, in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure., Comment: 11 pages, 2 figures, submitted to J. Chem. Phys

We study whether the stationary state of two bulk-driven systems slowly exchanging particles can be described by the equality of suitably defined nonequilibrium chemical potentials. Our main result is that in a weak contact limit, chemical potentials can be defined when the dynamics of particle exchange takes a factorized form with respect to the two systems, and satisfies a macroscopic detailed balance property at large deviation level. The chemical potentials of systems in contact generically differ from the nonequilibrium chemical potentials of isolated systems, and do not satisfy an equation of state. Yet, classes of systems satisfying the zeroth law of thermodynamics can be defined in a natural way. These results are illustrated on a driven lattice particle model and on an active particle model. The case when a chemical potential cannot be defined also has interesting consequences, like a non-standard form of the grand-canonical ensemble., Comment: 7 pages, 1 figure

We study a mass transport model on a ring with parallel update, where a continuous mass is randomly redistributed along distinct links of the lattice, choosing at random one of the two partitions at each time step. The redistribution process on a given link depends on the masses on both sites, at variance with the Zero Range Process and its continuous mass generalizations. We show that the steady-state distribution takes a simple non-factorized form that can be written as a sum of two inhomogeneous product measures. A factorized measure is recovered for a symmetric mass redistribution, corresponding to an equilibrium process. A non-equilibrium free energy can be explicitly defined from the partition function. We evaluate different characterizations of the `distance' to equilibrium, either dynamic or static: the mass flux, the entropy production rate, the Gibbs free-energy difference between the equilibrium and non-equilibrium stationary states, and the derivative of the non-equilibrium free energy with respect to the applied driving force. The connection between these different non-equilibrium parameters is discussed., Comment: 18 pages

We investigate the drying dynamics of porous media with two pore diameters separated by several orders of magnitude. Nanometer-sized pores at the edge of our samples prevent air entry, while drying proceeds by heterogeneous nucleation of vapor bubbles (cavitation) in the liquid in micrometer-sized voids within the sample. We show that the dynamics of cavitation and drying are set by the interplay of the deterministic poroelastic mass transport in the porous medium and the stochastic nucleation process. Spatio-temporal patterns emerge in this unusual reaction-diffusion system, with temporal oscillations in the drying rate and variable roughness of the drying front., Comment: Supplemental Material and Supplemental Movie available at http://www.stroockgroup.org/home/publications

We analyze thermodynamic bounds on equilibrium fluctuations of an order parameter, which are analogous to relations, which have been derived recently in the context of non-equilibrium fluctuations of currents. We discuss the case of {\it global} fluctuations when the order parameter is measured in the full system of interest, and {\it local} fluctuations, when the order parameter is evaluated only in a sub-part of the system. Using isometric fluctuation theorems, we derive thermodynamic bounds on the fluctuations of the order parameter in both cases. These bounds could be used to infer the value of symmetry breaking field or the relative size of the observed sub-system to the full system from {\it local} fluctuations., Comment: 8 pages, 6 figures, in press for Europhys. Lett