Related papers: Information entropy and complexity measure in gene…
Though Shannon entropy of a probability measure $P$, defined as $- \int_{X} \frac{\ud P}{\ud \mu} \ln \frac{\ud P}{\ud\mu} \ud \mu$ on a measure space $(X, \mathfrak{M},\mu)$, does not qualify itself as an information measure (it is not a…
An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…
We derive a connection between performance of estimators the performance of the ideal observer on related detection tasks. Specifically we show how Shannon Information for the task of detecting a change in a parameter is related to the…
In this work, we use the Shannon informational entropies to study an electron confined in a double quantum dot; we mean the entropy in the space of positions, $S_r$, in the space of momentum, $S_p$, and the total entropy, $S_t = S_r+S_p$.…
In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization…
Building on Shannon's lead, let's consider a more malleable expression for tracking uncertainty, and states of "knowledge available" vs. "knowledge missing," to better practice innovation, improve risk management, and successfully measure…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…
This presentation's Part 3 studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the…
Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…
The work is devoted to study of the following problem: can we use any qualitative criteria for realization of such universal phenomenon as self-organization in open systems? We have defined values of information at fixed points of…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
Fisher information ($I$) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate $r$ and $p$ spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as…
We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…
We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…
Complex frequency excitations, oscillating signals whose amplitude decreases exponentially in time, have recently been demonstrated to significantly increase the effective quality factor of mechanical resonators. In this work, we…
Quantum Fisher Information (QFI) is a ubiquitous quantity with applications ranging from quantum metrology and resource theories to condensed matter physics. In equilibrium local quantum many-body systems, the QFI of a subsystem with…
Accurately determining dependency structure is critical to discovering a system's causal organization. We recently showed that the transfer entropy fails in a key aspect of this---measuring information flow---due to its conflation of dyadic…