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Field Theory Entropy, the -theorem and the Renormalization Group
We consider entropy and relative entropy in Field theory and establish
relevant monotonicity properties with respect to the couplings. The relative
entropy in a field theory with a hierarchy of renormalization group fixed
points ranks the fixed points, the lowest relative entropy being assigned to
the highest multicritical point. We argue that as a consequence of a
generalized theorem Wilsonian RG flows induce an increase in entropy and
propose the relative entropy as the natural quantity which increases from one
fixed point to another in more than two dimensions.Comment: 25 pages, plain TeX (macros included), 6 ps figures. Addition in
title. Entropy of cutoff Gaussian model modified in section 4 to avoid a
divergence. Therefore, last figure modified. Other minor changes to improve
readability. Version to appear in Phys. Rev.
The maximum entropy state
We give an algorithm for calculating the maximum entropy state as the least
fixed point of a Scott continuous mapping on the domain of classical states in
their Bayesian order.Comment: 15 page
Anti-de-Sitter-Maxwell-Yang-Mills black holes thermodynamics from nonlocal observables point of view
In this paper, we analyze the thermodynamic properties of the Anti de Sitter
black hole in the Einstein-Maxwell-Yang-Mills-AdS gravity (EMYM) via many
approaches and in different thermodynamical ensembles (canonical/ grand
canonical). First, we give a concise overview of this phase structure in the
entropy-thermal diagram for fixed charges then we investigate this
thermodynamical structure in fixed potentials ensemble. The Next relevant step
is recalling the nonlocal observables such as holographic entanglement entropy
and two-point correlation function to show that both observables exhibit a Van
der Waals-like behavior in our numerical accuracy and just near the critical
line as the case of the thermal entropy for fixed charges by checking Maxwell's
equal area law and the critical exponent. In the light of the grand canonical
ensemble, we also find a newly phase structure for such a black hole where the
critical behavior disappears in the thermal picture as well as in the
holographic one.Comment: 23 pages, 9 figures, Advances in High Energy Physics accepted versio
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