Related papers: Exact correspondence between Renyi entropy flows a…
In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…
Despite recent claims we argue that Renyi's entropy is an observable quantity. It is shown that, contrary to popular belief, the reported domain of instability for Renyi entropies has zero measure (Bhattacharyya measure). In addition, we…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
Inertial range energy transfer in three dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two point statistics, exact relations corresponding to the energy cascade are…
The Renyi entropy with a free Renyi parameter $q$ is the most justified form of information entropy, and the Tsallis entropy may be regarded as a linear approximation to the Renyi entropy when $q\simeq 1$. When $q\to 1$, both entropies go…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, then the value of the Shannon entropy comes to formally…
We demonstrate supersymmetry in the counting statistics of stochastic particle currents and use it to derive exact nonperturbative relations for the statistics of currents induced by arbitrarily fast time-dependent protocols.
We calculate the ratio eta/s, the shear viscosity (eta) to entropy density (s), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The mean-field results of…
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact.…
We revisit entropy methods to prove new sharp trace logarithmic Sobolev and sharp Gagliardo-Nirenberg-Sobolev inequalities on the half space, with a focus on the entropy inequality itself and not the actual flow, allowing for somewhat…
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary…
Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences,…
The nature of particle and entropy flow between two superfluids is often understood in terms of reversible flow carried by an entropy-free, macroscopic wavefunction. While this wavefunction is responsible for many intriguing properties of…
This paper attempts to construct monotonic entropy functionals for four-dimensional Lorentzian spacetime under physical boundary conditions, as an extension of Perelman's monotonic entropy functionals constructed for three-dimensional…
Entanglement entropy is a measure of quantum correlations between separate parts of a many-body system, which plays an important role in many areas of physics. Here we review recent work in which a relation between this quantity and the…
We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and the total energy. For these systems, we construct a relative…
In recent years, the Renyi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Renyi entropy is studied. A compact general formula is presented for the lower…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…