written by Kostas Papamichalis

This simulation shows the diffusion of N particles along a 1-dimensional finite lattice, towards the state of equilibrium. The particles are distributed in a sequence of cells arranged along the lattice. In a time-interval of length Dt, each particle can perform just one jump between neighboring cells with a certain transition probability determined in the frame of the Ehrenfest model. The initial state of the system and the number of the cells along the lattice, are selected by the user. In a sequence of time-moments, the program of the simulation calculates the number of particles in every cell. The number of the particles in a cell is depicted by a certain cell-color. The intermediate states of the system between the initial state and the final state of equilibrium are depicted by a varying histogram and a sequence of changing cell-colors.

The theoretical distribution of the particles at the equilibrium state is depicted in the same system of axes. The first objective of the simulation is to compare the data obtained in real-time from the virtual environment, with the theoretical predictions of the model. Furthermore, as a second objective, the user is able to confirm the theoretical proposition that "irrespectively of the form of the initial distribution, the system converges to a certain equilibrium state which is determined by the transition probabilities". In a separate window, the graph of a Lyapunov functional H corresponding to the system, is created in real time. Each time-moment, the value of H is uniquely determined by the corresponding distribution of the particles in the cells of the lattice. In addition, by observing the graph of H over time, the user can estimate the relaxation time of the process towards the equilibrium state.

• Download webejs_model_The_Ehrenfest_Diffusion_Model_in_1-D_Lattice.zip - 846kb Compressed File

Released under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 license.

Published December 18, 2025
Last Modified December 28, 2025

Description of the Ehrenfest Diffusion on a 1D Lattice moldel.

• Download EhrenfestDiffusionModel.pdf - 441kb Adobe PDF Document

Last Modified December 28, 2025

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WebEJS source code for the  Ehrenfest Diffusion Model on a 1D Lattice model.

• Download webejs_src_The_Ehrenfest_Diffusion_Model_in_1-D_Lattice.zip - 489kb Compressed File

Last Modified December 28, 2025