Formulating the statistical mechanics for a non-minimal scalar field in a black hole background we propose modification of the original ’t Hooft “brick wall” prescription. Instead of the Dirichlet condition we suggest some scattering ansatz for the field functions at the horizon. This modifies the energy spectrum of the system and allows one to obtain the correct dependence of the statistical e...

the second law of thermodynamic (entropy principle) is of special theo-philosophical importance. it seems that this law, which is renowned as “the death of software design” and despite the order in the world, is like an incompatible universal. this article examines the concept of entropy in the three temperature, statistic, and information applications and addresses the contradiction of the sec...

A (k, ε)-non-malleable extractor is a function nmExt : {0, 1}×{0, 1} → {0, 1} that takes two inputs, a weak source X ∼ {0, 1} of min-entropy k and an independent uniform seed s ∈ {0, 1}, and outputs a bit nmExt(X, s) that is ε-close to uniform, even given the seed s and the value nmExt(X, s′) for an adversarially chosen seed s′ 6= s. Dodis and Wichs (STOC 2009) showed the existence of (k, ε)-no...

We derive an Itô stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equalit...

As a causality criterion we propose the conditional relative entropy. The relationship with information theoretic functionals mutual information and entropy is established. The conditional relative entropy criterion is compared with 3 well-established techniques for causality detection: ‘Sims’, ‘GewekeMeese-Dent’ and ‘Granger’. It is shown that the conditional relative entropy, as opposed to th...

Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addition, some matrix trace inequalities related to the Tsallis relative entropy are studied.

One method for building classification trees is to choose split variables by maximising expected entropy. This can be extended through the application of imprecise probability by replacing instances of expected entropy with the maximum possible expected entropy over credal sets of probability distributions. Such methods may not take full advantage of the opportunities offered by imprecise proba...

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of either isolated Hamiltonian evolution, or Markovian dynamics in open systems. However, there is no reason a priori why the Markovian appr...