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The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process…
The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete,…
In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation,…
Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…
The purpose of this comment is to correct mistaken assumptions and claims made in the paper Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations by T. D. Frank. Our comment centers on the claims…
The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we…
The accurate determination of transport coefficients in numerical simulations is becoming increasingly important in a wide range of applications. Here we consider the linear response in systems driven away from thermal equilibrium into a…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and…
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with $N$ species, $M$ reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical…
Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they often do not respect the laws of…
This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…