This phenomenon occurs as the relevant two body interaction is not tempered and is not H-stable. For 10 points each:
[10h] Name this phenomenon that David Lynden-Bell invoked to explain core collapse. This phenomenon is often explained by obtaining a heat capacity from the virial theorem.
ANSWER: gravothermal catastrophe [or gravothermal collapse or Antonov instability; prompt on catastrophe; prompt on instability; prompt on gravity]
[10e] Catastrophic configurations forbid the existence of a thermodynamic limit that allows one to define one of these constructs. The Helmholtz type of these constructs is proportional to the logarithm of the partition function.
ANSWER: free energy
[10m] The thermodynamic limit also guarantees the equivalence of these probability distributions in phase-space. Gibbs introduced one of these constructs which defines a constant energy surface.
ANSWER: thermodynamic ensembles
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