  The quest for ever higher information capacities has brought about a
renaissance in multimode optical waveguide systems. This resurgence of interest
has recently initiated a flurry of activities in nonlinear multimode fiber
optics. The sheer complexity emerging from the presence of a multitude of
nonlinearly interacting modes has led not only to new opportunities in
observing a host of novel optical effects that are otherwise impossible in
single-mode settings, but also to new theoretical challenges in understanding
their collective dynamics. In this Article, we present a consistent
thermodynamical framework capable of describing in a universal fashion the
exceedingly intricate behavior of such nonlinear highly multimoded photonic
configurations at thermal equilibrium. By introducing pertinent extensive
variables, we derive new equations of state and show that both the 'internal
energy' and optical power in many-mode arrangements always flow in such a way
so as to satisfy the second law of thermodynamics. The laws governing
isentropic processes are derived and the prospect for realizing Carnot-like
cycles is also presented. In addition to shedding light on fundamental issues,
our work may pave the way towards a new generation of high power multimode
optical structures and could have ramifications in other many-state nonlinear
systems, ranging from Bose-Einstein condensates to optomechanics.
