Density Fluctuations and Phase Behaviour in Non-Equilibrium Systems
type: CreativeWork
description: There is an established theoretical framework within equilibrium statistical physics, where the underlying physical laws are microscopically reversible in time. For such systems, the Boltzmann probability distribution explicitly governs the space of all possible configurations, allowing a thorough understanding of their physical behaviour. In nature, however, thermal equilibrium is more an exception than a rule. Most biological systems are inherently out of equilibrium: the self-propelling nature of organisms such as birds and bacteria, or the existence of an extinction state easily breaks the principle of detailed balance and places the underlying physical system outside of thermal equilibrium. The absence of time reversibility usually prevents calculation of an explicit probability distribution. Nevertheless, there have been significant advances in the development of theories to describe non-equilibrium systems. A major theme is to employ a dynamical field theoretic approach, where coarse-grained density fields evolve via stochastic partial differential equations that encode the spatiotemporal evolution of the system. These field theories can be constructed in two directions: either bottom-up, by coarse-graining the microscopic rules of particle motion, or top-down, by imposing conservation laws and symmetries. This thesis addresses two types of phase behaviour, each described by dynamical field theories developed via one of the two approaches. The first concerns phase transitions into absorbing states, which are configurations that the system can reach but cannot leave. We focus on a class of such transitions that are coupled to particle number conservation and infinitely many absorbing states: the random organisation (RO) universality class. This class connects closely to one encompassing a wide range of models, including conserved sandpiles and growth of elastic interfaces under disordered media. Using renormalisation group analysis in the Doi-Peliti formalism,…
abstract: There is an established theoretical framework within equilibrium statistical physics, where the underlying physical laws are microscopically reversible in time. For such systems, the Boltzmann probability distribution explicitly governs the space of all possible configurations, allowing a thorough understanding of their physical behaviour. In nature, however, thermal equilibrium is more an exception than a rule. Most biological systems are inherently out of equilibrium: the self-propelling nature of organisms such as birds and bacteria, or the existence of an extinction state easily breaks the principle of detailed balance and places the underlying physical system outside of thermal equilibrium. The absence of time reversibility usually prevents calculation of an explicit probability distribution. Nevertheless, there have been significant advances in the development of theories to describe non-equilibrium systems. A major theme is to employ a dynamical field theoretic approach, where coarse-grained density fields evolve via stochastic partial differential equations that encode the spatiotemporal evolution of the system. These field theories can be constructed in two directions: either bottom-up, by coarse-graining the microscopic rules of particle motion, or top-down, by imposing conservation laws and symmetries. This thesis addresses two types of phase behaviour, each described by dynamical field theories developed via one of the two approaches. The first concerns phase transitions into absorbing states, which are configurations that the system can reach but cannot leave. We focus on a class of such transitions that are coupled to particle number conservation and infinitely many absorbing states: the random organisation (RO) universality class. This class connects closely to one encompassing a wide range of models, including conserved sandpiles and growth of elastic interfaces under disordered media. Using renormalisation group analysis in the Doi-Peliti formalism,…
author: Ma, Xiao
language: eng
keywords: Soft Matter, Non-Equilibrium Statistical Mechanics, Renormalisation Group, Pattern Formation, Field Theories
license: https://www.repository.cam.ac.uk/bitstreams/dd8b8661-d7f5-41d3-8afe-d54edc4080c1/download
license: http://purl.org/NET/rdflicense/allrightsreserved
date published: 2025-06-30
date modified: 2026-07-22T22:24:10Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.122000