A Characterization of the Entropy--Gibbs Transformations

a characterization of the entropy--gibbs transformations

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...

Boltzmann-gibbs Entropy: Axiomatic Characterization and Application

Wepresent axiomatic characterizations of both Boltzmann andGibbs entropies together with an application.

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Entropy of infinite systems and transformations

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

Gibbs Entropy and Irreversibility

This contribution is dedicated to dilucidating the role of the Gibbs entropy in the discussion of the emergence of irreversibility in the macroscopic world from the microscopic level. By using an extension of the Onsager theory to the phase space we obtain a generalization of the Liouville equation describing the evolution of the distribution vector in the form of a master equation. This formal...

Gibbs' Paradox and the Definition of Entropy

Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adopting Boltzmann’s definition of the entropy, the violation of the second law is eliminated, the properties of co...