Related papers: An introduction to phase transitions in stochastic…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between…
We study the steady state of a three-level system in contact with a non-equilibrium environment, which is composed of two independent heat baths at different temperatures. We derive a master equation to describe the non-equilibrium process…
The stationary points of the potential energy function V are studied for the \phi^4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
Recently it is shown that there are three families of stochastic one-dimensional non-equilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states…
We consider a nonequilibrium process on a timeline with discrete sites which evolves by a non-Markovian update rule in such a way that an active site at time t activates one or several sites in the future at time t+dt. The time intervals dt…
We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here one does not have a partition function, instead we consider the zeros of a steady-state normalization…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
The nonequilibrium dynamic phase transition in ferromagnetic systems is reviewed. Very recent results of dynamic transition in kinetic Ising model and that in Heisenberg ferromagnet is discussed.
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium states. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to…
Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
Dynamical phase transitions are defined through non-analyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude. By…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…