Related papers: Variational principle for weakly dependent random …
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
For a given topological dynamical system $(X,T)$ over a compact set $X$ with a metric $d$, the "variational principle" states that \begin{equation*} \sup_{\mu}h_\mu(T) = h(T) = h_d(T), \end{equation*} where $h_\mu(T)$ is the…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
We introduce a new minimisation principle for Poisson equation using two variables: the solution and the gradient of the solution. This principle allows us to use any conforming finite element spaces for both variables, where the finite…
This article consists of two parts. The main objectives of Part 1 are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
In this paper, three laws are obtained for multiple-input multiple-output feedback systems, which are in entropy domain, frequency domain, and time domain, respectively. The system setup is that with causal plants and causal controllers.…
We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the $N$$\times$$\infty$ quasi-one-dimensional…
The simple L\'evy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the…
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when…
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
The entropy per particle in most Monte-Carlo simulations is size dependent due to correlated energy fluctuations. Guided by nanothermodynamics, we find a constraint for the Ising model that enhances the fluctuations and lowers the free…
The Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution $P(h_{i})=p\; \delta(h_{i}-h_{0}) + q \delta (h_{i}+ \lambda *h_{0}) + r \delta (h_{i})$, is investigated. The…
Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of…
We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator…
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…
This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable Systems", by the same authors.
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We use the Gaussian variational principle to apply cMERA to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian…