let h be a finite dimensional complex hilbert space, b(h)+ be the set of all positive semi-definite operators on h and phi is a (not necessarily linear) unital map of b(h) + preserving the entropy-gibbs transformation. then there exists either a unitary or an anti-unitary operator u on h such that phi(a) = uau* for any b(h) +. thermodynamics, a branch of physics that is concerned with the study...

We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending repulsion strength $\beta$ between different signs an activity parameter $\lambda$ particles. analyse Gibbsian properties time-evolved intermediate Gibbs measure static model, under spin-flip time evolution, in regime large $\beta$. ...

The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs has an O(1/T ) convergence rate for models with independent variables and for fully connected probabilistic graphical models. Herded Gibbs is shown to outperfo...

The present work analyzes the foundations of Gibbs’ thermodynamic equilibrium theory, with the general aim of understanding how the Second Law—as formulated by Clausius in 1865—has been embodied into Gibbs’ formal system and extended to processes involving chemical reactions. We show that Gibbs’ principle of maximal entropy (and minimal energy) is the implicit expression of Clausius’ Second Law...

the steps taken in designing a loop reactor for bulk propylene polymerization are discussed. the roles played by several parameters like particle growth factor, catalyst activity and solid fraction on reactor volume at different operating conditions are investigated. at first, based on a fixed production capacity and specific rate of catalyst, reactor volume is determined. next, the length and ...