Related papers: A Hamiltonian approach to the gradient-flow equati…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the…
The equation of motion for a point particle in the background field of double field theory is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by analysis on the particle motion, we…
We study the gradient flow of an energy with mixed homogeneity which is at the interface of Finsler and sub-Riemannian geometry
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…
This paper proposes a new equation from continuous adjoint theory to compute the gradient of quantities governed by the Transport Theory of light. Unlike discrete gradients ala autograd, which work at the code level, we first formulate the…
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\it capacitary measures} with respect to the…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by…
The Hamiltonian operator describing a quantum particle on a path often extends holomorphically to a complex neighborhood of the path. When it does, it can be seen as the local expression of a complex projective structure, and its…
Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and…
We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to…
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…