Related papers: Gouy-Stodola Theorem as a variational principle fo…
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…
We study the motion of isentropic gas in nozzles. This is a major subject in fluid dynamics. In fact, the nozzle is utilized to increase the thrust of rocket engines. Moreover, the nozzle flow is closely related to astrophysics. These…
The present paper reports our attempt to search for a new universal framework in nonequilibrium physics. We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
In this paper we advance the entropy theory of discrete nonautonomous dynamical systems that was initiated by Kolyada and Snoha in 1996. The first part of the paper is devoted to the measure-theoretic entropy theory of general topological…
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium…
For thermostatted dissipative systems the Fluctuation Theorem gives an analytical expression for the ratio of probabilities that the time averaged entropy production in a finite system observed for a finite time, takes on a specified value…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium…
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This…
We examine a discrete model of sticky particles initially subjected to acceleration. We propose a novel generalized variational principle for characterizing clusters (i.e., particle agglomerations) under decreasing acceleration function.…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on {\it ad hoc} definitions of the…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
It is shown by simple and straightforward considerations that discreteness of basic physical variables is, at least, essential for generalized statistical mechanics with non-logarithmic entropy to be thermodynamically applicable to…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
Several implications of well-known fluctuation theorems, on the statistical properties of the entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a…