Related Experiment Video
Updated: Sep 26, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
Poincaré cycle of a multibox Ehrenfest urn model with directed transport
1National Center for High-Performance Computing, No. 21, Nan-ke 3rd Road, Hsin-Shi, Tainan County 744, Taiwan, Republic of China.
Abstract:
We propose a generalized Ehrenfest urn model of many urns arranged periodically along a circle. The evolution of the urn model system is governed by a directed stochastic operation. Method for solving an N-ball, M-urn problem of this model is presented. The evolution of the system is studied in detail. We find that the average number of balls in a certain urn oscillates several times before it reaches a stationary value. This behavior seems to be a peculiar feature of this directed urn model. We also calculate the Poincaré cycle, i.e., the average time interval required for the system to return to its initial configuration. The result indicates that the fundamental assumption of statistical mechanics holds in this system.
Related Concept Videos
Reynolds Transport Theorem
Hückel's Rule Diagram of π MOs: Frost Circle
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
Multicompartment Models: Overview
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
Poisson's And Laplace's Equation
First Law: Particles in One-dimensional Equilibrium
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 path...
