Remarks about the thermodynamics of astrophysical systems in mutual interaction and related notions

Abstract

.Aspects concerning the thermodynamics of astrophysical systems are discussed, generally, and also more specifically those relating to astrophysical systems in mutual interaction (or the so-called open astrophysical systems). A special interest is devoted in this paper to clarifying several misconceptions that are still common in the recent literature, such as the direct application to the astrophysical scenario of notions and theoretical frameworks that were originally conceived to deal with extensive systems of everyday practice (large systems with short-range interactions). This discussion starts by reviewing the current understanding of the notion of negative heat capacity. Beyond this, to clarify its physical relevance, the conciliation of this notion with classical fluctuation theory is discussed, as well as equilibrium conditions concerning systems with negative heat capacities. These results prompt a revision of our understanding about critical phenomena, phase transitions and the so-called zeroth law of thermodynamics. Afterwards, general features about the thermodynamics of astrophysical systems are presented through the consideration of simple models available in the literature. Particular attention is devoted to the influence of evaporation on the macroscopic behavior of these systems. These antecedents are then applied to a critical approach towards the thermodynamics of astrophysical systems in mutual interaction. It is discussed that the long-range character of gravitation leads to the incidence of long-range correlations. This peculiarity imposes a series of important consequences, such as the non-separability of a single astrophysical structure into independent subsystems, the breakdown of additivity and conventional thermodynamic limit, a great sensibility of the macroscopic behavior to the external conditions, the restricted applicability of the so-called thermal contact in astrophysics, and hence, the non-relevance of conventional statistical ensembles in this scenario. To clarify how some of conventional notions and theoretical frameworks could be extended to open astrophysical systems, an exploratory study of a paradigmatic situation is presented: a binary astrophysical system. This analysis is carried out in the framework of the quadrupole approximation, which represents the lowest coupling among internal and collective degrees of freedom. Apparently, collective motions are responsible for a non-linear energy interchange among the astrophysical systems. This mechanism introduces some modifications in stationary and stability conditions for the thermodynamic equilibrium such as a generalization of Thirring’s stability condition for systems with negative heat capacities (1970 Z. Phys. 235 339). Additionally, the stability of collective motions of this binary astrophysical system is also discussed, which is related to the low energy thermodynamic behavior of the model discussed by Votyakov and colleagues (2002 Phys. Rev. Lett. 89 031101). The thermodynamic limit for self-gravitating gas of identical non-relativistic point particles is then derived and compared with other different proposals. The astrophysical counterpart of the Gibbs–Duhem relation is obtained and compared with the recent proposal of Latella and colleagues (2015 Phys. Rev. Lett. 114 230601). Finally, the incidence of non-extensivity during the merger of two identical astrophysical systems is analyzed. Contrary to the situation considered in the Gibbs paradox, the merger is an irreversible process that crucially depends on the existence (or non-existence) of the external gravitational influence of other systems.