Kinetic theory and hydrodynamics of cosmic strings

Abstract

We develop further a kinetic theory of strings and derive a transport equation for a network of cosmic strings with Nambu-Goto evolution, interactions, and background gravitational effects taken into account. We prove an $H$-theorem and obtain necessary and sufficient conditions for a thermodynamic equilibrium. At the lowest order, the equilibrium is estimated by the von Mises-Fisher distributions, parametrized by mean directions and dispersions of the right- and left-moving tangent vectors. Under assumption of a local equilibrium, we derive a complete set of hydrodynamic equations that govern the evolution of strings on large scales. We also argue that on small scales, the assumption of a local equilibrium would break down, so nonequilibrium steady states, described by the Sinai-Ruelle-Bowen distributions, should be used instead.