  The complex nonlinear behaviors of heavily multimode lightwave structures
have been recently the focus of considerable attention. Here we develop an
optical thermodynamic approach capable of describing the thermalization
dynamics in large scale nonlinear photonic chain networks - a problem that has
remained unresolved so far. A Sackur-Tetrode equation is obtained that
explicitly provides the entropy of these systems in terms of all the extensive
variables involved. This entropic description leads to a self-consistent set of
equations of state from where the optical temperature and chemical potential of
the photon gas can be uniquely determined. Processes like isentropic
expansion/compression, Joule expansion, as well as aspects associated with beam
cleaning/cooling and thermal conduction effects in such chain networks are
discussed. Our results open new vistas through which one can describe in an
effortless manner the exceedingly complex dynamics of highly multimoded
nonlinear bosonic systems that are nowadays of importance in areas ranging from
high-power photonic settings to cold atom condensates and optomechanics.
