相关论文: Non-Gaussian PDFs from Maximum-Entropy-principle c…
Supplement 1 to GUM (GUM-S1) recommends the use of maximum entropy principle (MaxEnt) in determining the probability distribution of a quantity having specified properties, e.g., specified central moments. When we only know the mean value…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…
There are two components in this work that allow solutions of the turbulent channel problem: one is the Galilean-transformed Navier-Stokes equation which gives a theoretical expression for the Reynolds stress; and the second the maximum…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
We unify two approaches that have been taken to explain the non-Gaussian probability distribution functions (PDFs) obtained in measurements of longitudinal velocity differences in turbulence, and we apply our approach to Couette-Taylor…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
The present paper is meant to give a simple introduction to the problem of the connection between microscopic dynamics and statistical laws. For sake of simplicity, we mostly refer to non-dissipative dynamics, since dissipation adds…
The macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow for a suitable mechanical system. Turbulent fluctuations (intermittency) then correspond to thermal fluctuations,…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
Superstatistics [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a superposition of…
A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to…
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk…
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow…
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy. Statistical equilibrium states are obtained by maximizing…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…