Related papers: A variational principle for holomorphic correspond…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
We consider homogenization of random surfaces and study the variational principle for graph homomorphisms from subsets of $\mathbb{Z}^m$ into $\mathbb{Z}$, where the underlying uniform measure is perturbed by a random field. Motivated by…
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…
Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the…
Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…
This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
Standard spectral codes for full sphere dynamics utilize a combination of spherical harmonics and a suitableradial basis to represent fluid variables. These basis functions have a rotational invariance not present ingeophysical flows.…
We study the dynamics of the metrics generated by measure preserving transformations. We consider a sequence of average metrics and define the corresponding sequence of $\epsilon$-entropies ({\it scaling sequence}) of the measure with…
We compare the entropy as a function of energy of excited strings and black strings in an asymptotically plane wave background at the level of the correspondence principle. For the plane wave supported by the NSNS 3-form flux, neither the…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends…
This paper defines and discusses the dimension notion of topological slow entropy of any subset for Z^d actions. Also, the notion of measure-theoretic slow entropy for Z^d actions is presented, which is modified from Brin and Katok [2].…
We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to…
Let f be a meromorphic correspondence on a compact Kahler manifold. We show that the topological entropy of f is bounded from above by the logarithm of its maximal dynamical degree. An analogous estimate for the entropy on subvarieties is…