Related papers: Network representations of non-equilibrium steady …
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…
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…
The evolution of physical systems are often modeled by simple Markovian processes. When settled into stationary states, the probability distributions of such systems are time independent, by definition. However, they do not necessarily fall…
One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we…
We investigate the structure of non-equilibrium steady states (NESS) for a class of exactly solvable models in the setting of a chain with left and right reservoirs. Inspired by recent results on the harmonic model, we focus on models in…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…
We review various combinatorial interpretations and mappings of stationary-state probabilities of the totally asymmetric, partially asymmetric and symmetric simple exclusion processes (TASEP, PASEP, SSEP respectively). In these steady…
We establish a correspondence between two very general paradigms for systems that persist away from thermal equilibrium. In the first paradigm, a nonequilibrium steady state (NESS) is maintained by applying fixed thermodynamic forces that…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These `open Markov processes' serve as the building blocks for…
The one-dimensional totally asymmetric simple exclusion process (TASEP), a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of $L$ sites. The relaxation to the…
The connection between dissipation and symmetry breaking is a long-standing enigma in statistical physics. It is intimately connected to the quest of a non-equilibrium functional whose minimization gives the non-equilibrium steady state…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
We investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network…
We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas…
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
A resistor-network picture of transitions is appropriate for the study of energy absorption by weakly chaotic or weakly interacting driven systems. Such "sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled to a…