Renormalization Group Approach to Dissipative System

TL;DR

This paper introduces a novel renormalization group method combining geometrical, continuum, and holographic approaches to analyze dissipative systems and friction phenomena.

Contribution

It presents a new multi-faceted approach integrating geometrical, path integral, and holographic methods with renormalization to study dissipative systems.

Findings

New renormalization method for dissipative systems

Effective analysis of statistical fluctuations in friction phenomena

Integration of multiple theoretical frameworks

Abstract

In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a new method which has the following characteristic points: 1) the geometrical approach to the statistical mechanical system; 2) the continuum approach using Feynman's path integral (generalized version); 3) the holographic (higher-dimensional) approach; 4) the renormalization phenomenon takes place in order to treat the statistical fluctuation.