Themodynamical aspects of self-simlar relaxation evolution of dense star clusters

Occurrence of negative heat capacity has been predicted and reported for various systems of particles and objects. Examples are granular gases, plasmas, atomic- and molecular- clusters, self-gravitating systems (black holes, stars, star clusters), ... The Antonov's pioneering work assumed an isothermal sphere (a self-gravitating system described by Maxwellian distribution function of particles at constant temperature) enclosed by an adiabatic wall. The work showed no maximum entropy state can be achieved for the sphere beyond a certain large-density contrast between the center and edge. Without the wall, the system expands and particles flow from the dense core to the ambient. Due to the negative heat capacity and conservation of energy/particle, the core heats up and shrinks while the ambient gets sparse and elongates. Such toy model has helped astrophysicists/astronomers to understand the structures of dense star clusters (e.g. globular cluster). More sophisticated models have predicted the clusters can evolve in a self-similar fashion at the late stage of relaxation evolution. The present work discusses the thermodynamical aspects of the self-similar-evolution model compared to classical models, such as the isothermal sphere, polytropic sphere and King model.