  This paper presents an observation that under reasonable conditions, many
partial differential equations from mathematical physics possess three
structural properties. One of them can be understand as a variant of the
celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a
direct relation of irreversible processes to the entropy change. We show that
the properties imply various entropy dissipation conditions for hyperbolic
relaxation problems. As an application of the observation, we propose an
approximation method to solve relaxation problems. Moreover, the observation is
interpreted physically and verified with eight (sets of) systems from different
fields.
