Thermodynamics and Energy

Thermodynamic Analysis of the Three-Body Problem: Stability and Parameter Estimation

Authors: Zhi Cheng
Comments: 7 Pages.

The three-body problem, while unsolvable in closed form under classical mechanics, can be approached through thermodynamic principles to reveal stable macroscopic behavior despite microscopic dynamical chaos. This paper proposes a thermodynamic framework for analyzing three-body systems by treating them as idealized gas-like ensembles, where pressure (P), volume (V), and temperature (T) serve as key descriptors. We address the challenge of limited particle count (N=3) by rescaling the Boltzmann constant (k_B) to account for the internal degrees of freedom within stellar-mass bodies (~10u2075u2077 hydrogen atoms per star). For a case study of three solar-mass stars with mean separation of 10 AU, we derive a system temperature of ~5×10³ K (consistent with stellar surfaces) and a negligible kinetic pressure of 25 Pa. Incorporating gravitational interactions via the virial theorem yields a higher effective pressure (65 Pa), indicating the need for adjusted velocities or smaller system volumes to maintain equilibrium. This work demonstrates how thermodynamics can bypass classical instabilities to predict equilibrium states, offering a novel perspective on N-body celestial mechanics. To verify the feasibility of this thermodynamic approach in solving problems, this paper also applies the method to the densely populated stellar region at the Galactic Center of the Milky Way. Through thermodynamic analysis, it is found that the stellar density at the Galactic Center is extremely high, resulting in a very high kinetic temperature of the stars in this region. This implies that the Galactic Center radiates a significant amount of energy outward. However, calculations reveal that the external pressure on the Galactic Center is very low, meaning that the structure remains highly stable under gravitational confinement alone.
Category: Thermodynamics and Energy