This paper describes an investigation into possible chaotic behavior in a coupled-oscillator system and the possible control of this behavior for communications. The established mathematical models for these oscillator arrays are demonstrated to exhibit chaos when the coupling strength between oscillators is below the range for phase locking. The complexity and predictability of the array dynam...

We introduce a deterministic chaotic system—the Szilard Map—that encapsulates the measurement, control, and erasure protocol by which Maxwellian Demons extract work from a heat reservoir. Implementing the Demon’s control function in a dynamical embodiment, our construction symmetrizes Demon and thermodynamic system, allowing one to explore their functionality and recover the fundamental trade-o...

The brain works as a dynamic system to process information. Various challenges remain in understanding the connection between information and dynamics attributes brain. present research pursues exploring how characteristics of neural functions are linked dynamics. We attempt bridge (e.g., Kolmogorov-Sinai entropy) mutual Fisher information) metrics on stimulus-triggered stochastic populations. ...

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.

Different security notions of secret sharing schemes have been proposed by different information measures. Entropies, such as Shannon entropy and min entropy, are frequently used in the setting security notions for secret sharing schemes. Different to the entropies, Kolmogorov complexity was also defined and used in study the security of individual instances for secret sharing schemes. This pap...

As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity of the form x+qy = x+y+(1−q)xy is a characteristic property of Tsallis entropy. Rényi in [1] generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint. In this paper we show that there exists no generalization for Tsallis entropy, b...

Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of themost popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can...