Langevin equation for the collective motions of a binary astrophysical system

According to Thirring’s condition, the thermodynamic equilibrium is not possible between two systems with negative heat capacities. Since the existence of negative heat capacity is a rule rather an exception in astrophysics, we would like to analyze the possibility of the thermodynamic equilibrium for a paradigmatic astrophysical situation: the binary system. The possible explanation arises after decomposing the dynamical variables into internal and collective degrees of freedom, which enables us to reinterpret binary systems as two systems [Formula: see text] and [Formula: see text] that interact between them through a third low dimensional system [Formula: see text]. Our central result is the derivation of a Langevin equation to describe the dynamics of the collective degrees of freedom. Our preliminary analysis evidences that the proposed framework is able not only to describe the system stability, but also unstable processes, such as escape or collapse of the binary system. These processes crucially depend on the angular momentum, the quadrupole–orbit coupling among internal and collective degrees of freedom, as well as internal temperatures of each system.