ABSTRACT In this paper the entropy function of the matrix game has been considered as one of the objectives and formulate a new game model, named Entropy Matrix Goal Game Model. Non-linear programming model for each player has been established. The equilibrium condition on matrix game is based on expected pay-off, so this equilibrium condition might be violated by mixed strategies when replicat...

In the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior. We examine the relative entropy distance D,, between the true density and the Bayesian density and show that the asymptotic distance is (d / 2 X l o g n) + c, where d is the dimension of the paramete...

Observation of non-Abelian statistics for the e/4 quasiparticles in the ν = 5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localized quasiparticles, and, hence, an additional low temperature entropy. Recent experiments, which detect changes in the number of quas...

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s dec...

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 ...

The enthalpy and entropy of vacancy creation in solid argon are re-evaluated using the two-body force approximation. At the triple point, the resulting vacancy free energy is g, = 1900 -4.0 RTcaljmole vat. This does not agree well with previous calculations of g,, but agrees well with experimental values of g, obtained from the argon specific heat”’ C, (but not with the questionable values obta...

The structure of a self-similar group G naturally gives rise to a transformation which assigns to any probability measure μ on G and any word w in the alphabet of the group a new probability measure μ. If μ is a convex combination of μ and the δ-measure at the group identity, then the asymptotic entropy of the random walk (G,μ) vanishes; therefore, the random walk is Liouville and the group G i...

Let f : M → M be a C r-diffeomorphism, r ≥ 1, defined on a compact boundaryless d-dimensional manifold M , d ≥ 2, and let H(p) be the homoclinic class associated to the hyperbolic periodic point p. We prove that if there exists a C 1 neighborhood U of f such that for every g ∈ U the continuation H(p g) of H(p) is entropy-expansive then there is a Df-invariant dominated splitting for H(p) of the...

We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for non-degenerate sequences of Hecke eigenfunctions on quotients Γ\G/K, where G ' PGLd(R), K is a maximal compact subgroup of G and Γ < G is a lattice associated to a division algebra over Q of prime degree d. The primary novelty of the present paper is a new method of proving positive entropy of quantum limits, which avoids s...