Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced. First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The la...

Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon–Khinchin axioms and by violating the fourth, the so-called comp...

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...

Non-additive entropy measures are important for many applications. We study Havrda and Charvat entropy for record values and have shown that this characterizes the underlying distribution function uniquely. Also the non-additive entropy of record values has been derived in case of some specific distributions. Further we propose a generalized residual entropy measure for record value.

In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states, we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This leaves open the question of defining the entropy of macroscopic, but unscalable systems, such as gravitating bodies or systems where surface effects are importan...

The present work illustrates the variable viscosity of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear or...

Recently, the problem of privacy amplification with an active adversary has received a lot of attention. Given a shared n-bit weak random source X with min-entropy k and a security parameter s, the main goal is to construct an explicit 2-round privacy amplification protocol that achieves entropy loss O(s). Dodis and Wichs [DW09] showed that optimal protocols can be achieved by constructing expl...

The connection between Tsallis entropy for a multifractal distribution and Jackson’s q-derivative is established. Based on this derivation and definition of a homogeneous function, a q-analogue of Shannon’s entropy is discussed. q-additivity of this entropy is shown. We also define q-analogue of Kullback relative entropy. The implications of lattice structure beneath q-calculus are highlighted ...