Thermodynamics and Planetary Motion

In an earlier post, I had discussed a possible derivation of Kepler's Second Law of Planetary Motion within a quantum gravity setting. Kepler's Second Law states that for a planet in orbit around another the Sun under the influence of Newtonian gravity:

the line connecting the planet to the Sun sweeps out equal areas in equal time

The basic idea involves applying Haggard and Rovelli's result about the rate of evolution of a quantum mechanical system, according to which a system in equilibrium evolves in such a way as to pass through an equal number of states in equal time intervals. Quantum Gravity (of the Loop variety) tells us that the fundamental observable in a quantum theory of geometry is the area of a surface embedded within a given spacetime.

The area swept out by a planet during the course of its motion around the Sun is far greater than $ A \gg A_p $(the basic quantum of area, where $A_p = l_p^2$ is the Planck length). However, if classical geometry as described by (classical) general relativity arises from a more fundamental quantum theory, and consistency of any theory of quantum gravity would require this, then it is natural to assume that the macroscopic area $\delta A$ swept out of by a planet in a time $\delta t$ emerges from an ensemble of quanta of Planck areas. If one could argue that planetary motion corresponds to an "equilibrium" configuration of the gravitational field, then Haggard and Rovelli's result can be applied and we obtain Kepler's Second Law as a trivial consequence.The key notion, therefore, is that central force planetary motion can be described in the language of thermodynamics as corresponding to the equilibrium configuration of some system.

It has been shown repeatedly (starting with Jacobson's result in 1994) that the equations of General Relativity arise when one imposes the condition of local equilibrium on apparent horizons seen by accelerated observers at any given point in a spacetime. Newtonian gravity, in turn, arises as the weak field limit of GR. Thus one might expect that there should be a thermal description of the behavior of masses in Newtonian gravity.

Thermal description of Newtonian orbits

In what precise sense, can one think of planetary orbits as equilibrium configurations?

Consider two objects which