29 - Short review of basic thermodynamics

Summary

Concepts

So far, we have followed two broad avenues of insight into the instability and clustering of infinite gravitating systems: linear kinetic theory and numerical N-body simulations. Now we turn onto a third avenue: thermodynamics. Classical thermodynamics is a theory of great scope and generality. It survived the relativity and quantum mechanical revolutions of physics nearly intact. In part, this was because among all theories of physics thermodynamics has the least physical content. Its statements relate very general quantities which must be defined anew, through equations of state, for each specific application. With this view, it is natural to ask whether thermodynamics also subsumes gravitating systems.

The answer is yes, with certain caveats and qualifications. Results of gravitational thermodynamics – gravithermodynamics, or GTD for short – are often surprising and counter-intuitive compared to the thermodynamics of ordinary gases. Specific heats, for example, can be negative and equilibrium is a more distant ideal. Basically, these differences are caused by the long-range, unsaturated (unshielded) nature of gravitational forces. As a result, rigorous understanding of GTD is less certain than for ordinary thermodynamics. The present situation is a bit similar to the early thermodynamic gropings of Watt, Carnot, Kelvin and Joule.

Straightforward introduction of gravity into thermodynamics leads again to the Jeans instability from a new point of view. It links up with linear kinetic theory and provides new insight into non-linear clustering.