Related papers: Information Shift Dynamics Described by Tsallis $q…
The gain-loss coupling in optical cavities induces exceptional points (EPs), where two optical modes coalesce. The large modal overlap near an EP intensifies gain competition, favoring single-mode lasing. Recent studies further revealed…
We investigate the mixed spin-$(s,\tfrac12)$ Ising model on a Cayley tree of order three ($k=3$), extending the approach of \cite{Akin2024}. For the representative case $s=5$, the associated recursion leads to an 11-dimensional dynamical…
We introduce `PI-Entropy' $\Pi(\tilde{\rho})$ (the Permutation entropy of an Indexed ensemble) to quantify mixing due to complex dynamics for an ensemble $\rho$ of different initial states evolving under identical dynamics. We find that…
In this paper we provide a full topological and ergodic description of the dynamics of Filippov systems nearby a sliding Shilnikov orbit. More specifically we prove that the first return map, defined nearby this orbit, is topologically…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…
In this work, we study the information scrambling and the entanglement dynamics in the complex Brownian Sachdev-Ye-Kitaev (cBSYK) models, focusing on their dependence on the charge density $n$. We first derive the effective theory for…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase…
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic…
We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an…
The maximum entropy principle is largely used in thresholding and segmentation of images. Among the several formulations of this principle, the most effectively applied is that based on Tsallis non-extensive entropy. Here, we discuss the…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with…
We consider the Ising, and more generally, $q$-state Potts Glauber dynamics on random $d$-regular graphs on $n$ vertices at low temperatures $\beta \gtrsim \frac{\log d}{d}$. The mixing time is exponential in $n$ due to a bottleneck between…
We prove that a shift ergodic measure on a topologically mixing sub-shift is isomorphic to a Bernoulli shift whenever it is quasi invariant under permutations of finite number of coordinates. We prove also that Gibbs measures on…
We investigate the critical behavior of continuous phase transitions in the context of Ginzburg Landau models with a double well effective potential. In particular, we show that the recently proposed configurational entropy, a measure of…
We experimentally study a gas of $N = 8$ one-dimensional Brownian particles, each confined in a harmonic trap with identical stiffness. The stiffness switches simultaneously between two values at random Poissonian times. This collective…
The entanglement and localization in eigenstates of strongly chaotic subsystems are studied as a function of their interaction strength. Excellent measures for this purpose are the von-Neumann entropy, Havrda-Charv{\' a}t-Tsallis entropies,…