1,721,024 research outputs found
A Weyl entropy of pure spacetime regions
Full text linkWe focus on the Penrose’s Weyl curvature hypothesis in a general framework encompassing many specific models discussed in literature. We introduce a candidate density for the Weyl entropy in pure spacetime perfect fluid regions and show that it is monotonically increasing in time under very general assumptions. Then we consider the behavior of the Weyl entropy of compact regions, which is shown to be monotone in time as well under suitable hypotheses, and also maximal in correspondence with vacuum static metrics. The minimal entropy case is discussed too
Homogeneity: From Caratheodory's approach to Gibbs thermodynamics
No full textWe consider thermodynamics of homogeneous systems in the frame-
work of Carath ́odory’s approach. We work in a configuration space where independent variables are all extensive, and we show that the requirement for homogeneity symmetry of the integrable 1-form δQrev , which represents the infinitesimal heat exchanged reversibly by a thermodynamic system, allows to find immediately and explicitly an integrating factor by means of elementary tools of differential geometry. The foliation of the thermodynamic manifold is associated in a natural way with an extensive potential, which is then identified with the metrical entropy S. Both S and the absolute temperature T are derived quantities in this framework. The entropy S corresponds to the fundamental relation in the entropy representation according to Gibbs’ approach to thermodynamics, thus an explicit connection between Carath ́odory’s approach and Gibbs’ approach to thermodynamics is obtained. The relation with statistical mechanical formalism is also pointed out
- …
