Violations of conservation laws in viscous liquid dynamics

Abstract

The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover, although particle number conservation applies strictly for any liquid, the solidity of viscous liquids implies that even this conservation law is apparently violated in coarse-grained descriptions of density fluctuations.

Acknowledgments

This work was supported by the Danish National Research Foundation's centre for viscous liquid dynamics ‘Glass and Time’.

Notes

†The Debye–Stokes–Einstein relation does not always apply, but the occasional 1–3 order of magnitude deviations do not affect the argument presented here. See, e.g. 15–18.

†Phenomenologically, one often defines a solid as a system which does not flow, implying that a ‘solid’ that ‘flows’ is a contradiction in terms. Whether a system flows or not, however, is a matter of time-scale; even a crystal flows at finite temperature. In a gravitational field, for instance, a vertically flat crystalline sample has lower free energy than, e.g., a cubic-shaped sample. Since any crystal in thermal equilibrium contains point defects, and since their movements are impeded only by finite energy barriers, ‘flow’ from the cubic-shaped sample to the flat is not only possible but bound to take place over sufficiently long time-scales.