Dissipation in equations of motion of scalar fields

The methods of non-equilibrium quantum field theory are used to investigate the possibility of representing dissipation in the equation of motion for the expectation value of a scalar field by a friction term, such as is commonly included in phenomenological inflaton equations of motion. A sequence of approximations is exhibited which reduces the non-equilibrium theory to a set of local evolution equations. However, the adiabatic solution to these evolution equations which is needed to obtain a local equation of motion for the expectation value is not well defined; nor, therefore, is the friction coefficient. Thus, a non-equilibrium treatment is essential, even for a system that remains close to thermal equilibrium, and the formalism developed here provides one means of achieving this numerically.