We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give unified and short proofs of various well known inequalities.

s of the talks Alexander Aptekarev, Keldysh Institut, Moscow (Russia) Title:” On a discrete entropy of ortogonal polynomials” Abstract: We shall discuss geometrical meaning of the discrete entropy of the eigenvector basis and particularly eigenvectors formed by orthogonal polynomials. The we present a nice new formula for the discrete entropy of Tchebyshev polynomials. It is joint work with J.S...

Random number generators (RNGs) are essential for cryptographic applications. In most practical applications, the randomness of RNGs is provided by entropy sources. If the randomness is less than the expected, the security of cryptographic applications could be undermined. Accurate entropy estimation is a critical method for the evaluation of RNG security, and significant overestimation and und...

σ ⊗n is given by a regularized quantum relative entropy distance formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes a novel operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite S...

The different contributions to the entropy change linked to the austenite-martensitic transition in a Ni-Mn-Sn metamagnetic shape memory alloy have been determined by combining different experimental techniques. The vibrational contribution has been inferred from the vibrational density of states of both the martensitic and austenite phases. This has been accomplished by combining time-of-fligh...

The natural outcome of the most striking similarity between the second laws of blackhole mechanics and thermodynamics is blackhole entropy. In this paper we discuss the evidence of blackhole entropy and the linearity relation between blackhole entropy to its horizon area. Finally, using thermodynamic relations we obtain Bekenstein-Hawking entropy, Hawking temperature and other intensive paramet...

The training of Neural Networks and particularly Multi-Layer Perceptrons (MLP's) is made by minimizing an error function usually known as "cost function". In our previous works, we apply the Error Entropy Minimization (EEM) algorithm in classification and its optimized version using, as cost function, the entropy of the errors between the outputs and the desired targets of the neural network. O...

Using gauge formulation of gravity the three-dimensional SU(2) YM theory equations of motion are presented in equivalent form as FRW cosmological equations. With the radiation, the particular (periodic, big bangbig crunch) three-dimensional universe is constructed. Cosmological entropy bounds (so-called Cardy-Verlinde formula) have the standard form in such universe. Mapping such universe back ...

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to ...

We argue that the thermodynamics of conformal field theories with AdS duals exhibits a remarkable universality. At strong coupling, a Cardy-Verlinde entropy formula holds even when R-charges or bulk supergravity scalars are turned on. In such a setting, the Casimir entropy can be identified with a generalized C-function that changes monotonically with temperature as well as when non-trivial bul...