Related papers: Granular entropy: Explicit calculations for planar…
he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy $\gamma$ and the excess adsorption $\Gamma$ are of central importance. For theoretical studies…
We establish a straightforward estimate for the number of open sets with fundamental group constraints needed to cover the total space of fibrations. This leads to vanishing results for simplicial volume and minimal volume entropy, e.g.,…
By making use of the entropy function formalism we study the generalized attractor equations in the four dimensional N=2 supergravity in presence of higher order corrections. This result might be used to understand a possible ensemble one…
It has been observed in both natural and man-made materials that volume sometimes decreases with increasing temperature. Though mechanistic understanding has been gained for some individual materials, a general answer to the question "Why…
We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike…
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show…
We introduce the notion of tubular dimension, and give a formula for it. As an application we show that every invariant measure of a $C^{1+\gamma}$ diffeomorphism of a closed Riemannian manifold admits an asymptotic local product structure…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
Entropy arises in strong interactions by a dynamical separation of ``partons'' from unobservable ``environment'' modes due to confinement. For interacting scalar fields we calculate the statistical entropy of the observable subsystem.…
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding…
We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces…
This work presents arbitrary high order well balanced finite volume schemes for the Euler equations with a prescribed gravitational field. It is assumed that the desired equilibrium solution is known, and we construct a scheme which is…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
We implement the Wang-Landau algorithm to sample with equal probabilities the static configurations of a model granular system. The "non-interacting rigid arch model" used is based on the description of static configurations by means of…
Stationary and isotropic iteration stable random tessellations are considered, which can be constructed by a random process of cell division. The collection of maximal polytopes at a fixed time $t$ within a convex window $W\subset{\Bbb…
Recently, it was proposed that a small true vacuum universe can inflate spontaneously, in principle. Furthermore, there should be matter creation in vacuum inflation due to quantum fluctuations, and the matter created will influence the…
arXiv:1205.2953 defines an entropy for a gaussian scalar field $\phi$ in an arbitrary region of either a causal set or a continuous spacetime, given only the correlator $\langle\phi(x)\phi(y)\rangle$ within the region. As a first…
In this paper we present a conjecture on the construction of generalised elliptic units above number fields with exactly one complex place. These elliptic units obtained as values of multiple elliptic Gamma functions. These form a…