36 research outputs found
A link between the maximum entropy approach and the variational entropy form
The maximum entropy approach operating with quite general entropy measure and
constraint is considered. It is demonstrated that for a conditional or
parametrized probability distribution there is a "universal"
relation among the entropy rate and the functions appearing in the constraint.
It is shown that the recently proposed variational formulation of the entropic
functional can be obtained as a consequence of this relation, that is from the
maximum entropy principle. This resolves certain puzzling points appeared in
the variational approach
Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems
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 power-law statistics are investigated. It is demonstrated
that, from a quite general point of view, the power-law dependencies may appear
as a consequence of "global" constraints restricting both the dynamic phase
space and the stochastic fluctuations. As a result, at sufficiently long
observation times the dynamic counterpart is driven into a non-equilibrium
steady state whose deviation from the usual exponential statistics is given by
the distance from the conventional equilibrium
On the double criticality of fluids adsorbed in disordered porous media
9 pages, 4 figuresThe phase transition of a fluid adsorbed in a heterogeneous system is studied with two simple lattice gas models within the framework of a mean-field theory. Despite the different origin of the heterogeneity (spatial variation of binding energy or fluid coordination numbers), the fluid can undergo two phase transitions if the hosting system is sufficiently heterogeneous. It is clearly shown that such a polymorphism in the confined fluid results from the successive condensations in distinct spatial regions of the host. We have found the precise conditions at which one two phase transitions occur. The insight gained from the present study allows one to understand better some recent puzzling simulation results