Thermodynamics and statistical mechanics of self-gravitating systems

It is not uncommon among scientists to consider philosophy of science to be an uninteresting distraction from more important matters. When it comes to the foundations of thermodynamics and statistical mechanics, however, some philosophers have made genuinely useful contributions, doing an excellent job of summarizing the current situation and bringing clarity to the strengths and weaknesses of different foundations. Jos Uffink’s article on what, strictly speaking, is asserted by the second law of thermodynamics comes to mind—it has been well received by both philosophers and physicists. To specialists in the field, there may not be much new, but philosophers have at the very least managed to provide clear presentations of successes and problems to a potential wider audience of philosophers, physicists, and lay-men.

I’d like to highlight two preprints by Callender and Wallace, respectively, on the subject of thermodynamics of self-gravitating systems. Statistical mechanics, as it is known to the majority of physicists, relies on the assumption that energy and entropy are extensive functions. This means that doubling a system (while keeping all intensive parameters—pressure, temperature, etc.—fixed) results in a doubling of energy and entropy. More generally, scaling the extensive parameters of a system by some (positive) factor should result in the energy and entropy of the system being scaled by the same factor. This assumption holds when there are no long-range interactions between subsystems, but it fails when there are significant gravitational interactions between subsystems. It is also unclear how what properties a thermodynamic equilibrium state (e.g. is it a maximum entropy state?) can be expected to have when gravitational effects are non-negligible. Callender discusses these and other problems in the statistical mechanics of self-gravitating systems. Since a statistical mechanics of self-gravitating systems must give up many results that hold in standard statistical mechanics, Callender also raises the question of how different the former can be from the latter and still be justifiably called “statistical mechanics”. Wallace discusses the related subject of what it actually means to take into account self-gravitational effects in thermodynamics. The discussion focuses on the cosmological example of the hot and near-uniform early state of the universe. In the absence of a clear theory of the thermodynamics of self-gravitational systems, cosmologists extrapolate intuitions developed from standard thermodynamics and the tentative view is that the early near-uniform state of the universe was a low-entropy state since gravitational effects favor a non-uniform lumpy state.


C. Callender. Hot and Heavy Matters in the Foundations of Statistical Mechanics. (2008) Rough draft available at the author’s homepage.

D. Wallace. Gravity, entropy, and cosmology: in search of clarity. (2009) phil-sci preprint 00004744


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