The equilibration of two coupled reservoirs is studied using a Green function approach which is suitable for future development with the closed time path method. The problem is solved in two parameterizations, in order to demonstrate the non-trivial issues of parameterization in both the intermediate steps and the interpretation of physical quantities. We use a covariant approach to find self-consistent solutions for the statistical distributions as functions of time. We show that by formally introducing covariant connections, one can rescale a slowly varying non-equilibrium theory so that it appears to be an equilibrium one, for the purposes of calculation. We emphasize the importance of properly tracking variable redefinitions in order to correctly interpret physical quantities.
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