相关论文: Universal Gorban's Entropies: Geometric Case Study

We analyze F\"urth's 1933 classical uncertainty relations in the modern language of stochastic differential equations. Our interest is motivated by applications to non-equilibrium classical statistical mechanics. We show that F\"urth's…

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is…

A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of…

We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…

We fix the temperature $T$ and consider mean energy and Boltzmann-Gibbs-Shannon entropy as two players of a game. As a result, basic formulas for the ordinary quantum mean energy and the Boltzmann-Gibbs-Shannon entropy are derived. We…

This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…

Comparing the representations learned by different neural networks has recently emerged as a key tool to understand various architectures and ultimately optimize them. In this work, we introduce GULP, a family of distance measures between…

In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the structure of the underlying network through Lyapunov functions…

Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…

In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…

We study convergence of nonlinear systems in the presence of an `almost Lyapunov' function which, unlike the classical Lyapunov function, is allowed to be nondecreasing---and even increasing---on a nontrivial subset of the phase space.…

Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…

Boltzmann introduced in the 1870's a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His entropic functional for classical systems was…

The thermodynamical entropy of a system which consists of different kinds of ideal gases is known to be defined successfully in the case when the differences are described by classical or quantum theory. Since these theories are special…

Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…

We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently…

An ab-initio calculation scheme for finite nuclei based on self-consistent Green's functions in the Gorkov formalism is developed. It aims at describing properties of doubly-magic and semi-magic nuclei employing state-of-the-art microscopic…

We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the…

It is shown that the structure of non-equilibrium thermodynamic system far from equilibrium can be captured in terms of a generalized "Nambu dynamics", in the presence of fluctuation effects in non-equilibrium thermodynamics. Triangular…

In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…