Related papers: Maximum caliber is a general variational principle…
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…
We adapt the statistical mechanics of the shallow-water equations to the case where the flow is forced at small scales. We assume that the statistics of forcing is encoded in a prior potential vorticity distribution which replaces the…
The statistical mechanical description of two-dimensional inviscid fluid turbulence is reconsidered. Using this description, we make predictions about turbulent flow in a rapidly rotating laboratory annulus. Measurements on the continuously…
A theory to predict the steady state position of a dissipative, flow-controlled system, as defined by a control volume, is developed based on the Maximum Entropy (MaxEnt) principle of Jaynes, involving minimisation of a generalised free…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
The flexibility of common generalized gradient approximation for the exchange-correlation energy is investigated by monitoring the equilibrium volume of transition metals. It is shown that no universal gradient-level approximation yielding…
In a recent paper, Phys. Rev E 81, 041137 (2010), the author attempts to derive ten necessary conditions for stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been…
We consider the modeling of the effect of unresolved scales, for two-dimensional and geophysical flows. We first show that the effect of small scales on a coarse-grained field, can be approximated at leading order, by the effect of the…
Mixture models are an expressive hypothesis class that can approximate a rich set of policies. However, using mixture policies in the Maximum Entropy (MaxEnt) framework is not straightforward. The entropy of a mixture model is not equal to…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
In this work we have obtained Maxwell-type equations for a compressible fluid which sources are functions of velocity and vorticity. A correlation function and the dispersion relation were analyzed as function of the Reynolds number. A…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance…
Theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids are investigated. Mean-field models are considered first but shown to be inadequate. An alternate approach is then studied in which each statistical…