Related Experiment Video
Updated: Oct 17, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Simple models for strictly non-ergodic stochastic processes of macroscopic systems
G George1, L Klochko1, A N Semenov1
1Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France.
Abstract:
We investigate simple models for strictly non-ergodic stochastic processes [Formula: see text] (t being the discrete time step) focusing on the expectation value v and the standard deviation [Formula: see text] of the empirical variance [Formula: see text] of finite time series [Formula: see text]. [Formula: see text] is averaged over a fluctuating field [Formula: see text] ([Formula: see text] being the microcell position) characterized by a quenched spatially correlated Gaussian field [Formula: see text]. Due to the quenched [Formula: see text]-field [Formula: see text] becomes a finite constant, [Formula: see text], for large sampling times [Formula: see text]. The volume dependence of the non-ergodicity parameter [Formula: see text] is investigated for different spatial correlations. Models with marginally long-ranged [Formula: see text]-correlations are successfully mapped on shear stress data from simulated amorphous glasses of polydisperse beads.
Related Concept Videos
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Mechanistic Models: Compartment Models in Individual and Population Analysis
Mechanistic Models: Overview of Compartment Models
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Cyclic Processes And Isolated Systems
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
Entropy

