Related papers: Generalized statistical mechanics for superstatist…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. There has been given the connection between conditions of superstability…
Plasmas and other systems with long-range interactions are commonly found in non-equilibrium steady states that are outside traditional Boltzmann-Gibbs statistics, but can be described using generalized statistical mechanics frameworks such…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
We introduce a rigorous framework for stochastic cell transmission models for general traffic networks. The performance of traffic systems is evaluated based on preference functionals and acceptable designs. The numerical implementation…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic…
In this paper I will review some basic aspects of the mechanism of stochastic resonance. Stochastic resonance was first introduced as a possible mechanism to explain long term climatic variation. Since then, there have been many…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
The existence of fluctuations of temperature has been a somewhat controversial topic in thermodynamics but nowadays it is recognized that they must be taken into account in small, finite systems. Although for nonequilibrium steady states…
In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…
Complex nonequilibrium systems are often effectively described by a `statistics of a statistics', in short, a `superstatistics'. We describe how to proceed from a given experimental time series to a superstatistical description. We argue…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
Statistical modeling of data sets by neural-network techniques is offered as an alternative to traditional semiempirical approaches to global modeling of nuclear properties. New results are presented to support the position that such novel…