Path integral approach to fluctuations in relativistic transport

In this paper we analyze the fluctuations in an approximation to relativistic heat transport theory from a path integral approach. We start with a telegraphist type equation for the heat transport derived from a Meixner–Prigogine scheme and construct a classical variational principle for it. We use Hamiltonian-like function to obtain the transition probability between two different non-equilibrium states. We show that this probability obeys the Chapman–Kolmogorov equation.