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We consider relaxation of an isolated system to the equilibrium using detailed balance condition and Onsager's fluctuation approximation. There is a small deviation from the equilibrium in two parameters. For this system, explicit…
Many have speculated whether nonequilibrium systems obey principles of maximum or minimum entropy production. In this work, we use stochastic thermodynamics to derive the condition for the minimum entropy production state (MEPS) for…
The Kolmogorov-Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the…
The Boltzmann distribution connects the energetics of an equilibrium system with its statistical properties, and it is desirable to have a similar principle for non-equilibrium systems. Here, we derive a variational principle for the…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
Many modern techniques employed in physics, such a computation of path integrals, rely on random walks on graphs that can be represented as Markov chains. Traditionally, estimates of running times of such sampling algorithms are computed…
Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states : the principle is to maximize the Shannon entropy…
We show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs…
In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
Physical and chemical stochastic processes described by the master equation are investigated. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master…
Steady-state flow of an incompressible fluid in parallel pipes can simultaneously satisfy two contradictory extremum principles in the entropy production, depending on the flow conditions. For a constant total flow rate, the flow can…
The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are…
Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
It is shown that Onsager's principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is…
The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate $h_{\mathrm{KS}}$ given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we…
The entropy production rate is a central quantity in non-equilibrium statistical physics, scoring how far a stochastic process is from being time-reversible. In this paper, we compute the entropy production of diffusion processes at…