Related papers: Information theory and renormalization group flows
We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated to the operation of increment of summands and rescaling. In this structure…
In this paper we analyze the renormalization group (RG) flow of field theories with quenched disorder, in which the couplings vary randomly in space. We analyze both classical (Euclidean) disorder and quantum disorder, emphasizing general…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time…
The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is…
We present the $T$-flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature $T$ of its environment. This has the key advantage that…
A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information $\mathcal{I}_N$ in a Hamiltonian system of large particle number…
Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…
Information diagram and the I-measure are useful mnemonics where random variables are treated as sets, and entropy and mutual information are treated as a signed measure. Although the I-measure has been successful in machine proofs of…
We develop a new formulation of the functional renormalization group (RG) for interacting fermions. Our approach unifies the purely fermionic formulation based on the Grassmannian functional integral, which has been used in recent years by…
At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…
The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
Using a novel approach to renormalization in the Hamiltonian formalism, we study the connection between asymptotic freedom and the renormalization group flow of the configuration space metric. It is argued that in asymptotically free…
We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is…
It is generally accepted that, when moving in groups, animals process information to coordinate their motion. Recent studies have begun to apply rigorous methods based on Information Theory to quantify such distributed computation.…
We study two dimensional freely decaying magnetohydrodynamic turbulence. We investigate the time evolution of the probability law of the gauge field and the stream function. Assuming that this probability law is initially defined by a…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
Haros graphs have been recently introduced as a set of graphs bijectively related to real numbers in the unit interval. Here we consider the iterated dynamics of a graph operator $\cal R$ over the set of Haros graphs. This operator was…
It is demonstrated that the renormalization group (RG) flows of depinning transitions do not depend on whether the driving force or the system velocity is kept constant. This allows for a comparison between RG results and corresponding…