Related papers: A Dynamic Theory of Information and Entropy
The information entropy is here investigated in the context of early and late cosmology under the hypothesis that distinct phases of universe evolution are entangled between them. The approach is based on the \emph{entangled state ansatz},…
We introduce a constructive framework for assigning thermodynamic structure to an arbitrary data system from its measured microstates. Starting from an empirical distribution over configurations, we first infer a data-driven energy function…
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…
Resent works of Hawking and Susskind suggested that information is conserved in the universe. We extend this thesis and propose that dynamics of information - computations can conserve in Anti-de-Sitter cosmological model. Information…
The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some---the ephemeral information---is dissipated and some---the bound information---is actively stored and so affects future behavior. We derive…
Information plays a pivotal role in the thermodynamics of nonequilibrium processes with feedback. However, much remains to be learned about the nature of information fluctuations in small scale devices and their relation with fluctuations…
We provide here a novel algebraic characterization of two information measures associated with a vector-valued random variable, its differential entropy and the dimension of the underlying space, purely based on their recursive properties…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by E. Verlinde's paper, we first calculate the…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
We focus attention on some particular thermodynamic relations (PTR). Using information theory concepts we show that, for a reversible process, microscopic considerations related to these PTR make the concomitant informational contents of…
Information theory has been taken as a prospective tool for quantifying the complexity of complex networks. In this paper, we first study the information entropy or uncertainty of a path using the information theory. Then we apply the path…
We aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure quantum field theory forces to consider a shared information between two different…
The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits,…
We generally consider that entropy and temperature of a spherically symmetric black hole are corrected by quantum effect. We calculate interior entropy variation of massless scalar field and compare it with corrected Bekenstein-Hawking…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…