The increase of entropy upon release of a constraint in classical systems

Abstract

Computer simulations have focused renewed attention on holonomic constraints imposed on selected coordinates for simplified effective calculations, and also for maintaining and parameterizing equilibrium states. Novel theoretical means for calculating thermodynamic potentials have recently been developed. Here, spontaneous transitions caused by the release of a constraint are treated on the same basis. To describe spontaneous changes, a parameter-like coordinate is converted into a dynamic generalized coordinate. The analysis yields, depending on the boundary conditions employed during the transition, a decrease in the free energy or, at constant energy, an increase in the entropy. This finding is in agreement with observations in computer simulation, and compatible with general theorems on the effect of interventions. The applicability of constraints to experimental setups is discussed using examples.

Acknowledgements

The author thanks M. Klähn, J. König and T. Mülders for helpful comments, and P. R. L. Markwick for help with English.