A strange black box

Compared to laboratory situations, a self-gravitating star cluster is a very strange object. Imagine that you were handed a star cluster in a closed box, so that you could only measure the temperature at the surface of the box. Imagine also that you could change the conditions of the star cluster from the outside in two ways: (1) you could put the box inside a larger box with a different temperature, as an effective heat bath, in order to change the temperature inside; (2) you could change the size of the box, compressing or expanding its volume.

So far, there is nothing unusual, and we might still pretend that we are about to carry out a textbook thermodynamics experiment. But when we dip our box into a heat bath, something strange may occur: depending on the exact conditions inside the box, the box may exhibit a most bizarre behaviour. When placed in a colder environment, the box may actually heat up, without limit. The only way to cool the box back to its original temperature would be to place it temporarily inside an even hotter environment – but not for too long, otherwise it will cool to below its original temperature.

This contrary tendency of self-gravitating systems corresponds to the fact that such systems can exhibit a negative heat capacity. We will return to this mysterious character later on, when we analyse its effects in detail, both on macroscopic scales, governing the evolution of a star cluster as a whole, and on a microscopic scale, when we deal with few-body systems.