The Statistical Mechanics of a Recent Gravitational Experiment

Plastino A and Rocca MC

Published on: 2025-09-04

Abstract

We obtain the approximate expression that describes two little masses that, simultaneously,

• Interact classically vie Newton-gravitation and
• Harmonically vibrate.

Note that in this case the partition function is always positive, as it should be, and the entropy is negative, meaning an increase in order in the system. But it should be noted that despite the entropy being negative, it is increasing, indicating that the system tends to become disordered. At the same time, we observe that the specific heat of the system is positive, indicating then that the system is not self-gravitating.

This is surprising, since it indicates that gravity behaves statistically very differently for extremely small masses than for large masses [7]. For large masses the specific heat has a divergence and a phase transition. For extremely small masses no.