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The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…
Equilibrium statistical mechanics provides a robust framework for characterizing phase transitions in systems whose microsopic dynamics are time-reversible. Efforts to develop and validate theoretical frameworks for time-irreversible,…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being inter-connected with each other. Using…
Diagrammatic approach proposed many years ago for strong correlated Hubbard model is developed for analyzing of the thermodynamic potential properties. The new exact relation between such renormalized quantities as thermodynamic potential,…
Mott variable range hopping is a fundamental mechanism for low-temperature electron conduction in disordered solids in the regime of Anderson localization. In a mean field approximation, it reduces to a random walk (shortly, Mott random…
We report, for the first time, the observation of ballistic thermal transport in a nonintegrable classical many-body system. This claim is substantiated by appropriately incorporating long-range interactions into the system, which exhibits…
For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system…
We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature…
A closed-loop control of a reaction-diffusion type process is introduced. The control system consist of a finite number of control and measurement devices. The measurement devices collect information about the current state of the process.…
We investigate heat transport through an assembly consisting of a two-level system coupled between two harmonic oscillators, which is described by the quantum Rabi model, as a prototype of nanoscale heat devices using controllable…
A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base…
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
This paper is concerned with the construction of several stochastic processes in a star graph, that is a non-euclidean structure where some features of the classical modelling fail. We propose a model for trapping phenomena with…
We study quadratic skew-products with parameters driven over piecewise expanding and Markov interval maps with countable many inverse branches, a generalization of the class of maps introduced by Viana. In particular we construct a class of…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
In this paper, we extend a result of Kesten and Spitzer (1979). Let us consider a stationary sequence $(\xi\_k:=f(T^k(.)))\_k$ given by an invertible probability dynamical system and some centered function $f$. Let $(S\_n)\_n$ be a simple…
Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper [1] is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…