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.

Keywords

Statistical Mechanics; Boltzmann-Gibbs Newtonian Gravity; Harmonic Oscillator

Introduction

Newtonian gravity is a fundamental classical theory, based on three fundamental laws, known as Newton’s laws of motion. It provides a reliable and accurate description of the motion of objects under normal everyday conditions.

Its key concept is the law of universal gravitation, which states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The gravitational constant, denoted by G, determines the strength of the gravitational force.

In addition to the law of universal gravitation, Newton’s laws of motion play a crucial role in understanding the behavior of objects in Newtonian gravity.

By combining these laws, Newtonian gravity allows us to predict the motion of objects under the influence of gravitational forces. It has been extremely successful in explaining the motion of celestial bodies in our solar system and played a crucial role in the development of classical physics. However, note that the Newtonian treatment constitutes (extremely good) approximation. It is not applicable in certain extreme conditions, such as near the speed of light or in the presence of very strong gravitational fields, where Einstein’s theory of general relativity becomes necessary.

When we delve into the realm of quantum mechanics and consider the behaviour of particles at very small scales, the concept of the “quantum limit” comes into play.

The quantum limit of Newton’s gravity refers to the point at which the predictions of classical Newtonian grav- ity break down and quantum effects become significant. At this scale, the behaviour of particles is described by quantum field theory, which incorporates both quantum mechanics and special relativity.

In quantum field theory, particles are described as excitations of their respective fields, such as the electromag- netic field or the Higgs field. These fields are quantized, meaning that their excitations, called particles, can only exist in discrete energy states. Particles also exhibit wave-particle duality, meaning they can behave as both particles and waves.

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