Abstract:
We discuss crystal formation in supersaturated suspensions of
monodisperse hard spheres with a concentration of hard spheres randomly pinned
in space and time. The pinning procedure introduces an external length scale
and an external time scale that restrict the accessible number of configureurations
and ultimately the number of pathways leading to crystallization. We observe a
significant drop in the nucleation rate density at a characteristic pinning
concentration that can be directly related to the structure of the critical
nucleus and the dynamics of its formation in the unpinned system.

Abstract:
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions both in their steady states and out of stationarity. Many reaction-diffusion systems have the peculiarity that microscopic reversibility is broken such that their transient behavior can not be investigated through the study of most of the observables discussed in the literature. For this reason we analyze the transient properties of reaction-diffusion systems through a specific work observable that remains well defined even in the absence of microscopic reversibility and that obeys an exact detailed fluctuation relation in cases where detailed balance is fulfilled. We thereby drive the systems out of their nonequilibrium steady states through time-dependent reaction rates. Using a numerical exact method and computer simulations, we analyze fluctuation ratios of the probability distributions obtained during the forward and reversed processes. We show that the underlying microscopic dynamics gives rise to peculiarities in the configuration space trajectories, thereby yielding prominent features in the fluctuation ratios.

Abstract:
We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic time reversibility. Studying a quantity that for an equilibrium system is related to the work done to the system, we observe that under certain conditions oscillations appear on top of an exponential behavior of transient fluctuation ratios. We argue that these oscillations encode properties of the probability currents in state space.

Abstract:
We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the crystalline phase (the crystalline phase directly appears without any induction time), while for stretched substrates we observe heterogeneous nucleation. The shapes of the nucleated crystallites fluctuate strongly. In the case of homogeneous nucleation amorphous precursors have been observed (Phys. Rev. Lett. {\bf 105}(2):025701 (2010)). For heterogeneous nucleation we do not find such precursors. The fluid is directly transformed into highly ordered crystallites.

Abstract:
We have carried out computer simulations of overcompressed suspensions of hard monodisperse ellipsoids and observed their crystallization dynamics. The system was compressed very rapidly in order to reach the regime of slow, glass-like dynamics. We find that, although particle dynamics become sub-diffusive and the intermediate scattering function clearly develops a shoulder, crystallization proceeds via the usual scenario: nucleation and growth for small supersaturations, spinodal decomposition for large supersaturations. In particular, we compared the mobility of the particles in the regions where crystallization set in with the mobility in the rest of the system. We did not find any signature in the dynamics of the melt that pointed towards the imminent crystallization events.

Abstract:
We discuss crystal formation in supersaturated suspensions of monodisperse hard spheres with a concentration of hard spheres randomly pinned in space and time. The pinning procedure introduces an external length scale and an external time scale that restrict the accessible number of configurations and ultimately the number of pathways leading to crystallization. We observe a significant drop in the nucleation rate density at a characteristic pinning concentration that can be directly related to the structure of the critical nucleus and the dynamics of its formation in the unpinned system.

Abstract:
Entropy production is one of the most important characteristics of non-equilibrium steady states. We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of non-equilibrium systems: transport systems and reaction-diffusion systems. The usefulness of the mean entropy production rate and of the large deviation function of the entropy production for characterizing non-equilibrium steady states of interacting many-body systems is discussed. We show that the large deviation function displays a kink-like feature at zero entropy production that is similar to that observed for a single particle driven along a periodic potential. This kink is a direct consequence of the detailed fluctuation theorem fulfilled by the probability distribution of the entropy production and is therefore a generic feature of the corresponding large deviation function.

Abstract:
Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $\alpha$ and death of the last particle $\delta$. The system presents a phase transition at $\delta_c(\alpha)$, where the average position of the last particle $$ grows as $\sqrt{t}$. For $\delta>\delta_c$, a non equilibrium stationary state exists while for $\delta<\delta_c$ the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.

Abstract:
We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.

Abstract:
We discuss the crystallization process from the supersaturated melt in terms of its non-equilibrium properties. In particular, we quantify the amount of heat that is produced irreversibly when a suspension of hard spheres crystallizes. This amount of heat can be interpreted as arising from the resistance of the system against undergoing phase transition. We identify an intrinsic compression rate that separates a quasi-static regime from a regime of rapid crystallization. In the former the disspated heat grows linearly in the compression rate. In the latter the system crystallizes more easily, because new relaxation channels are opened, at the cost of forming a higher fraction of non-equilibrium crystal structures. In analogy to a shear-thinning fluid, the system shows a decreased resistance when it is driven rapidly.