Stars and steam engines: To what extent do thermodynamics and statistical mechanics apply to self-gravitating systems?

Foundational puzzles surround (Newtonian) gravitational thermal physics—a realm in which stars are treated as akin to molecules in a gas. Whether such an enterprise is successful and the domain of thermal physics extends beyond our terrestrial sphere is disputed. There are successes (such as the collisionless Boltzmann equation) and paradoxical features (such as the ‘gravothermal catastrophe’). Callender (Found Phys 41(6):960–981, 2011) advocates reconciling the two sides of the dispute by taking a broader view of thermodynamics. Here I argue for an alternative position: if we are careful in distinguishing statistical mechanics and thermodynamics, then no reconciliation is required. Both sides can live in harmony because whilst statistical mechanics applies, thermodynamics does not. This state of affairs—the applicability of statistical mechanics without the emergence of thermodynamic behaviour—can be explained in terms of an infamous infinite idealisation: the thermodynamic limit.