Black hole entropy is studied for an exactly solvable model of two-dimensional gravity[1], using recently developed Noether charge techniques[2]. This latter approach is extended to accomodate the non-local form of the semiclassical effective action. In the two-dimensional model, the final black hole entropy can be expressed as a local quantity evaluated on the horizon. This entropy is shown to...

Abstract. We establish that for q ≥ 1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local e...

The coin-position entanglement generated by the evolution operator of a discrete–time quantum walk is quantified, using the von Neumann entropy of the reduced density operator (entropy of entanglement). In the case of a single walker, the entropy of entanglement converges, in the long time limit, to a well defined value which depends on the initial state. Exact expressions are obtained for loca...

This paper aims to perform the second law analysis of thermodynamics on the laminar film condensation of pure saturated vapor flowing in the direction of gravity on an ellipsoid with variable wall temperature. The analysis provides us understanding how the geometric parameterellipticity and non-isothermal wall temperature variation amplitude “A.” affect entropy generation during film-wise conde...

Every evolutionary algorithm needs to address two important facets: exploration and exploitation of a search space. Evolutionary search must combine exploration of the new regions of the space with exploitation of the potential solutions already identified. The necessity of balancing exploration with exploitation needs to be intelligent. This paper introduces an entropy-driven parameter control...

A generally relativistic theory of thermodynamics is developed, based on four main physical principles: heat is a local form of energy, therefore described by a thermal energy tensor; conservation of heat, or the local first law, equivalent to conservation of mass; entropy is a local current; and non-destruction of entropy, or the local second law. A fluid is defined by the thermostatic energy ...