Kinetic Theory and Hydrodynamics of Cosmic Strings

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, and non-equilibrium steady states, described by the Sinai-Ruelle-Bowen distributions, should be used instead.

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