Related papers: Nonequilibrium Statistical Operator for Systems of…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
We obtain a form of the local thermodynamic equilibrium density operator which is invariant under pseudo-gauge transformations of the stress-energy and the spin tensors. This operator is an excellent candidate to describe the dynamics of a…
We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the…
We propose predictive information, that is information between a long past of duration T and the entire infinitely long future of a time series, as a universal order parameter to study phase transitions in physical systems. It can be used,…
In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large…
The long-time behaviour of spin-spin correlators in the slow relaxation of systems undergoing phase-ordering kinetics is studied in geometries of finite size. A phenomenological finite-size scaling ansatz is formulated and tested through…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Though there is no convergence on the origin of time's preferential direction, many researchers…
A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an…
Functional inequalities such as the Poincar\'e and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to variance and entropy decay. However, many applications,…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
This paper establishes a natural quantum counterpart of weak equilibration for statistical ensembles in integrable systems. For quantum systems with pure point spectrum, single-time expectation values under unitary evolution are typically…
In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can…