Non-equilibrium Theory for Non-ergodic Systems Based on Time-and-Space Averaging

Explore a 54-minute lecture on non-equilibrium theory for non-ergodic systems using time-and-space averaging. Delve into the development of a theoretical approach that assumes ergodic conditions only at very small length scales, applicable to many non-ergodic systems. Learn how fluctuations are constrained by internal energy dynamics and how quasi-ergodic requirements can identify valid transport coefficient timescales. Discover the application of this theory to immiscible fluid flow through porous media, explaining non-Gaussian pressure fluctuations caused by capillary events. Understand how macroscopic dynamics can be homogenized by choosing appropriate averaging timescales and how fluid topology changes contribute to non-ergodic effects. Examine the role of time-and-space averages in accounting for discrete changes based on topological residence time. Cover topics such as geometric representation, ergodic theory, scale-consistent thermodynamics, conservation of energy, relative permeability, Darcy's law, and pressure fluctuations in this comprehensive exploration of non-equilibrium thermodynamics for non-ergodic systems.

Introduction
Main topic
Geometric picture
Topological changes
Droplet coalescence
Geometric representation
Ergotic theory
Nonergotic systems
What if the ergotic hypothesis doesnt hold
Discontinuities
Spatial heterogeneity
Scaleconsistent thermodynamics
Deviation terms
Simple example
More complicated example
Substituting thermal energy
Maxwells demon
Conservation of energy
Relative permeability
Energy barriers
Diffusive length scale
Energy conservation
homogenization
Darcys law
Crosscoupling terms
Simulations
Topology
Pressure fluctuations
Stationary vs nonstationary
Summary
Frequency dependence
Maxwell demon