NEGATIVE SPECIFIC-HEAT PARADOX

All astronomers know that when a star or a star cluster loses energy its temperature will increase in accordance with the virial theorem. Beckenstein & Hawking have demonstrated that black holes display the same phenomenon. Thus astronomical systems display negative specific heat. However, there is a simple proof in statistical mechanics that specific heats are positive. This paradox, first resolved by Thirring, is further explored with a simple model which obeys the virial theorem. The great differences that can arise between Gibbs's canonical ensembles and microcanonical ensembles are thereby further illustrated. If the model is treated canonically it shows a remarkable giant phase transition which replaces a wide zone of negative specific heat found by microcanonical approach. This behaviour suggested to us that the origin of all normal phase transitions may lie in negative-specific-heat elements that only arise at a microscopic level. A simple model of a chemical reaction or ionization demonstrates that this is a correct interpretation of these transitions. © Royal Astronomical Society.