Related Experiment Video
Updated: May 7, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Chaos and ergodicity of two hard disks within a circular billiard
Shin-ichi Sawada1, Tooru Taniguchi
1Department of Physics, Kwansei Gakuin University, Sanda 669-1337, Japan.
Abstract:
We investigate dynamical properties of the system of two interacting hard disks within a circular billiard numerically in the case of zero total angular momentum. Varying the radius of two identical disks, we examine chaotic irregularity and ergodicity of the system. Single-particle configuration and velocity distributions are obtained from dynamical trajectory calculations and compared with those in the microcanonical ensemble. We also analyze properties of trajectories by calculating the finite-time maximum Lyapunov exponent and clarify the existence of sticky motions around Kolmogorov-Arnold-Moser (KAM) tori even for small radii of disks. It is shown that the present system is almost ergodic in spite of the existence of tori for small radii of disks since the ratio of tori to the whole phase space is extremely small. On the other hand, a number of tori increase abruptly as the radius of disks increases beyond some value and tori prevent trajectories to run over the phase space uniformly, which makes the ergodicity of the system broken down.
More Related Videos
Related Concept Videos
Entropy and the Second Law of Thermodynamics
Entropy and the Second Law of Thermodynamics
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
The Entropy as a State Function
Conservation of Linear Momentum for a System of Particles
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
Entropy

