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Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to the...

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Related Experiment Video

Updated: Jun 8, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Exact on-event expressions for discrete potential systems.

Marcus N Bannerman¹, Leo Lue

¹School of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom. marcus.bannerman@cbi.uni-erlangen.de

The Journal of Chemical Physics

|October 5, 2010

Summary

This study reveals new analytical expressions for discrete potential systems, linking atomic event rates to thermodynamic properties like pressure and temperature, validated by simulations.

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Area of Science:

Physics
Physical Chemistry
Computational Science

Background:

Systems with discrete potentials exhibit unique atomic interaction dynamics.
Understanding these interactions is crucial for modeling various physical and chemical systems.
Existing models may not fully capture the kinetic energy distributions and thermodynamic relationships in such systems.

Purpose of the Study:

To derive closed analytical expressions for kinetic energy distribution functions in discrete potential systems.
To establish exact relationships between event rates and macroscopic thermodynamic properties (pressure, temperature).
To validate these derived expressions using event-driven molecular dynamics simulations.

Main Methods:

Derivation of analytical expressions for on-event kinetic energy distribution functions.
Formulation of exact equations relating system pressure and temperature to specific atomic event rates (core, bounce, dissociation/association).
Validation through event-driven molecular dynamics simulations of square-well/shoulder potential systems.

Main Results:

Novel analytical expressions for kinetic energy distributions, distinct from Maxwell-Boltzmann.
Exact relationships derived: pressure depends on core and bounce event rates; temperature on the ratio of bounce to dissociation/association events.
Simulations confirm the derived expressions' accuracy within statistical error.

Conclusions:

The study provides a new theoretical framework for understanding discrete potential systems.
Event rates offer a direct pathway to calculating thermodynamic properties, simplifying analysis.
The findings are broadly applicable to systems governed by discrete atomic interactions.