Related papers: System/environment duality of nonequilibrium obser…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
The Lindbladian formalism models open quantum systems using a 'bottom-up' approach, deriving linear dynamics from system-environment interactions. We present a 'top-down' approach starting with phenomenological constraints, focusing on…
We study a nonrelativistic system made of two quantum particles constrained to move on a line and a spin located at a fixed point of the line. Initially the two particles are in a maximally entangled state and the spin is down. The first…
The linear laws of transport phenomena are central in our description of irreversible processes in systems across the physical sciences. Linear irreversible thermodynamics allows for the identification of the underlying forces driving…
Despite significant progress on stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings in addressing multiagent systems with highly coupled…
We present a general formulation to calculate the dynamic optical conductivity, beyond the linear response regime, of any electronic system whose quasiparticle dispersion is described by a two band model. Our phenomenological model is based…
We present a summary of the applications of duality to Donaldson-Witten theory and its generalizations. Special emphasis is made on the computation of Donaldson invariants in terms of Seiberg-Witten invariants using recent results in N=2…
The opportunity of occurrence of entropy oscillations around of a stationary state in linear and nonlinear processes is theoretically shown. The new mechanism of global tendencies appearance is described.
This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS.We show that…
We explore a nonlinear extension to quantum theory giving rise to deterministic partial disentanglement between pairs of particles. The extension is based on a modified Schr\"{o}dinger equation having an added nonlinear term. To avoid…
In this paper we present an equivalent form of Granger noncausality in state space representation. As a generalization of this result, necessary and sufficient conditions are provided for an output process to admit a particular minimal…
This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
We develop a dual description of quantum optics adapted to dielectric systems without magnetic property. Our formalism, which is shown to be equivalent to the standard one within some dipolar approximations discussed in the article, is…
This paper considers the observability of nonlinear systems from a Koopman operator theoretic perspective--and in particular--the effect of symmetry on observability. We first examine an infinite-dimensional linear system (constructed using…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…