Related papers: Entropy, Dynamics and Instantaneous Normal Modes i…
In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
We derive an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…
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…
In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…
We consider lattice gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas…
Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo…
We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…
In low temperature supercooled liquid, below the ideal mode coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. We present a theory which incorporates interaction between the two processes and shows…
The introduced entropy functional's (EF) information measure of random process integrates multiple information contributions along the process trajectories, evaluating both the states' and between states' bound information connections. This…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic…
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…
We explore a method of statistical estimation called Maximum Entropy on the Mean (MEM) which is based on an information-driven criterion that quantifies the compliance of a given point with a reference prior probability measure. At the core…
We propose a statistical mechanics for a general class of stationary and metastable equilibrium states. For this purpose, the Gibbs extremal conditions are slightly modified in order to be applied to a wide class of non-equilibrium states.…