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 $f(x|\mu)$ 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

Interplay of host volume variations and internal distortions in the course of intercalation into disordered matrices

Based on a combination of the distortive lattice gas model and the maximum information entropy approach, the thermodynamics of insertion into disordered hosts is analyzed. It is found that the isotherm specificities can be explained as a cooperative interplay of the host volume expansion and the internal distortions, which tend to optimize the host structure inducing a local lowering of the insertion energetic cost. Behavior of amorphous Lix W O3 films of different thicknesses is discussed in this context

Ge-rich graded-index SiGe alloys: exploring a versatile platform for mid-IR photonics

International audienceIn this paper, the recent progress on a new Ge-rich SiGe platform for mid-IR integrated photonics is presented. Low-loss spiral waveguides working over a broadband wavelength range are discussed, followed by a sensing proof-of-concept using a standalone photoresist with a known spectral absorption pattern. In addition, the development of new mid-IR interferometric devices for wavelength filtering and enhancement of the light-matter interaction are presented. Finally, efficient designs to exploit the third-order nonlinearities in these Ge-rich SiGe waveguides at mid-IR wavelengths are shown. The demonstration of these key building blocks will pave the way towards the implementation of new mid-IR photonic integrated systems with multiple functionalities