Non-equilibrium Onsager-Machlup theory

Abstract

This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or \emph{"piecewise"}) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein-Uhlenbeck stochastic process (which is \emph{globally} stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager-Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear, and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager-Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the \emph{non-equilibrium self-consistent generalized Langevin equation} (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and the gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model.

References in corpus (23)

• Invariant Variation Problems
• Dynamic Density Functional Theory of Fluids
• Observation of empty liquids and equilibrium gels in a colloidal clay
• Classical dynamical density functional theory: from fundamentals to applications
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Mode-Coupling Theory of the Glass Transition: A Primer
• Interplay between Spinodal Decomposition and Glass Formation in Proteins Exhibiting Short-Range Attractions
• Liquid Limits: The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids
• Multiple Glasses in Asymmetric Binary Hard Spheres
• Elasticity of arrested short-ranged attractive colloids: homogeneous and heterogeneous glasses
• A closer look at arrested spinodal decomposition in protein solutions
• A New Theory of Dynamic Arrest in Colloidal Mixtures
• General Non-equilibrium Theory of Colloid Dynamics
• Noether's Theorem in Statistical Mechanics
• Aging of a Homogeneously Quenched Colloidal Glass-forming Liquid
• Simplified Self-Consistent Theory of Colloid Dynamics
• Glassy dynamics in asymmetric binary mixtures of hard-spheres
• Equilibration and aging of dense soft-sphere glass-forming liquids
• Relaxation dynamics in a transient network fluid with competing gel and glass phases
• Dynamical arrest: interplay of the glass and of the gel transitions
• Non-equilibrium Kinetics of the Transformation of Liquids into Physical Gels
• A framework of nonequilibrium statistical mechanics. II. Coarse-graining
• Waiting-time dependent non-equilibrium phase diagram of simple glass- and gel-forming liquids