  We investigate the dissipation rate of a scalar field in the vicinity of the
phase transition and the ordered phase, specifically within the universality
class of model A. This dissipation rate holds significant physical relevance,
particularly in the context of interpreting effective potentials as inputs for
dynamical transport simulations, such as hydrodynamics. To comprehensively
understand the use of effective potentials and other calculation inputs, such
as the functional renormalization group, we conduct a detailed analysis of
field dependencies. We solve the functional renormalization group equations on
the Schwinger-Keldysh contour to determine the effective potential and
dissipation rate for both finite and infinite volumes. Furthermore, we conduct
a finite-size scaling analysis to calculate the dynamic critical exponent z.
Our extracted value closely matches existing values from the literature.
