Related papers: Varentropy Decreases Under the Polar Transform
We study the instability of multiply charged vortices in the presence of thermal atoms and find various scenarios of splitting of such vortices. The onset of the decay of a vortex is always preceded by the increase of a number of thermal…
We analyze the saturation value of the bipartite entanglement and number entropy starting from a random product state deep in the MBL phase. By studying the probability distributions of these entropies we find that the growth of the…
Divergences that occur in density matrices of decay and scattering processes are shown to be regularized by tracing and unitarity or the optical theorem. These divergences are regularized by the lifetime of the decaying particle or the…
It has been observed in both natural and man-made materials that volume sometimes decreases with increasing temperature. Though mechanistic understanding has been gained for some individual materials, a general answer to the question "Why…
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…
In systems far from equilibrium, the statistics of observables are connected to entropy production, leading to the Thermodynamic Uncertainty Relation (TUR). However, the derivation of TURs often involves constraining the parity of…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
Achieving information-theoretic security using explicit coding scheme in which unlimited computational power for eavesdropper is assumed, is one of the main topics is security consideration. It is shown that polar codes are capacity…
In this work, we develop a generalisation of the thermal entropy to complex inverse temperatures, which we call the thermal pseudo-entropy. We show that this quantity represents the pseudo-entropy of the transition matrix between…
Understanding nonequilibrium systems and the consequences of irreversibility for the system's behavior as compared to the equilibrium case, is a fundamental question in statistical physics. Here, we investigate two types of nonequilbrium…
The polarization charge $\rho $ of an inhomogeneous superfluid system is expressed as a function of the order parameter $\Phi ({{\mathbf{r}}_{1}},{{\mathbf{r}}_{2}})$. It is shown that if the order parameter changes on macroscopic…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by…
The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each…
This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=\bigtriangleup x_i\bigtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured information of a…
We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a…
Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\mathbb{N}$ and consider a general a-priori probability for…
We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal…
In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are…