相关论文: Integrable Hierarchies and Information Measures
We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrodinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially…
An overview is presented of quantum and resonant nonlinear Schr\"odinger equation links to Whitham-Broer-Kaup type systems. A novel n+1-dimensional extension of the Whitham-Broer-Kaup hydrodynamic system is constructed with connection to an…
The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and…
A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…
We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality (Cie\'slak--Fuest--Hajduk--Sier\.z\k{e}ga, 2024),…
We work out the general theory of one-parameter families of partial entanglement properties and the resulting entanglement depth-like quantities. Special cases of these are the depth of partitionability, the depth of producibility (or…
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…
In this thesis, we investigate various integral submodels and generalize them. In part I, we study the submodel of the nonlinear $\mathbf{C}P^1$-model and the related submodels in $(1+2)$ dimensions. In part II, we construct integrable…
Landauer's principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro-…
Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $\phi$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we…
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation…
Normal geodesic flows flows of Carnot-Caratheodory are discussed from the point of view of the theory of Hamiltonian systems. The geodesic flows corresponding to left-invariant metrics and left- and -right-invariant rank 2 distributions on…
In this paper, we are concerned with the non-relativistic limit of a class of computable approximation models for radiation hydrodynamics. The models consist of the compressible Euler equations coupled with moment closure approximations to…
We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is…
The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in…
Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an…
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…
3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…