We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of equilibrium are derived. These transitions manifest themselves as singularities in the large deviation function, resulting in enhanced current fluctuations. Microscopic models which implement each of the scenarios are presented, with possible experimental realizations. Depending on the model, the singularity is associated either with a particle-hole symmetry breaking, which leads to a continuous transition, or in the absence of the symmetry with a first-order phase transition. An exact Landau theory which captures the different singular behaviors is derived.

Because active particles break time-reversal symmetry, a single non-spherical body placed in an active fluid generates currents. We show that when two or more passive bodies are placed in an active fluid these currents lead to long-range interactions. Using a multipole expansion we characterize their leading-order behaviors in terms of single-body properties and show that they decay as a power law with the distance between the bodies, are anisotropic, and do not obey an action-reaction principle. The interactions lead to rich dynamics of the bodies, illustrated by the spontaneous synchronized rotation of pinned non-chiral bodies and the formation of traveling bound pairs. The occurrence of these phenomena depends on tunable properties of the bodies, thus opening new possibilities for self-assembly mediated by active fluids.Active matter is a class of nonequilibrium systems in which energy is converted into systematic motion on a microscopic scale [1]. They have attracted much attention [2,3] due to a host of interesting physical phenomena [4][5][6][7][8][9], their relevance to many biological systems [10][11][12][13], and their potential use for self-assembly applications [14]. They have also been suggested as tools for novel engineering applications -for example, active fluids have been used to power microscopic gears [15][16][17][18][19][20][21]. This results from the fact that, when an asymmetric body is immersed in a fluid with broken time-reversal symmetry, it experiences a net force [22][23][24] which is coupled to the generation of ratchet-like currents [25,26].In this Letter we study passive bodies immersed in an active fluid. We show that the ratchet-like currents generated by each body give rise to forces and torques which decay as a power law with distance, are anisotropic, and do not obey an action-reaction principle. Using a multipole expansion, the leading-order behavior of the interactions can be expressed in terms of single-body quantities that can be measured independently in experiments or numerical simulations. Moreover, by designing the two bodies one can control the amplitude and polarity of the interactions between them. This leads to a host of interesting dynamical phenomena of which we illustrate two: the spontaneous synchronized rotations of pinned rotors and the formation of traveling bound pairs. Our results suggest a new method for self-assembly by embedding passive bodies in an active fluid.We stress that the interactions studied here exist even between non-moving bodies and are therefore distinct from usual hydrodynamic interactions [27]. They are also different from thermal Casimir interactions [28,29], because they do not rely on correlations between the fluid particles and are present even in a dilute active fluid.Model. -We base our study on a common model of an active fluid consisting of N point-like particles, which * y.baek@damtp.cam.ac.uk do not interact among themselves and self-propel at a constant speed v in two dimensions. The position r i and the orientation θ i of acti...

We study singularities in the large deviation function of the time-averaged current of diffusive systems connected to two reservoirs. A set of conditions for the occurrence of phase transitions, both first and second order, are obtained by deriving Landau theories. First-order transitions occur in the absence of a particle-hole symmetry, while second-order occur in its presence and are associated with a symmetry breaking. The analysis is done in two distinct statistical ensembles, shedding light on previous results. In addition, we also provide an exact solution of a model exhibiting a second-order symmetry-breaking transition. CONTENTS

Large deviation functions of configurations exhibit very different behaviors in and out of thermal equilibrium. In particular, they exhibit singularities in a broad range of non-equilibrium models, which are absent in equilibrium. These singularities were first identified in finite-dimensional systems in the weak-noise limit. Recent studies have shown that they are also present in driven diffusive systems with an infinite-dimensional configuration space. This short review describes singularities appearing in both types of systems under a unified framework, presenting a classification of singularities into two broad categories. The types of singularities which were identified for finite-dimensional cases are compared to those found in driven diffusive systems.