Variational principle for stochastic mechanics based on information measures

A Variational Principle for Quasistatic Mechanics

Quasistatic mechanical systems are those in which mass or acceleration are sufficientlysmall that the inertial term mu in F = mu is negligible compared to dissipative forces. In roboticsquasistatic mechanics may be used for systems with friction when motions are sufficiently slow. Here weconsider a general quasistatic system with constraints and both dissipative and conservative for...

Stochastic variational principle on riemannian manifolds

Variational Principle for Fuzzy Gibbs Measures

In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memoryless channels in information theory, continuous block factors of sym...

Variational principle for generalized Gibbsian measures

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and obtain a familiar expression in terms of entropy and relative energy for ”almost Gibbsian measures” (almost sure continuity of conditional probabilities). We ...

On the Variational Principle for Generalized Gibbs Measures

We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamic formalism for generalized Gibbs states will be discussed. A new class of intuitively Gibbs measures is introduced, and a typical example is studied. Finally, we present a new example of a non-Gibbsian measure arising from an industrial ap...