  Because of their massless nature, photons do not interact in linear optical
media. However, light beam propagation in nonlinear media permits to break this
paradigm, and makes it possible to observe photon-photon interactions. Based on
this principle, a beam of light propagating in a nonlinear multimode optical
system can be described as a gas of interacting particles. As a consequence,
the spatio-temporal evolution of this photon gas is expressed in terms of
macroscopic thermodynamic variables, e.g., temperature and chemical potential.
Moreover, the gas evolution is subject to experiencing typical thermodynamic
phenomena, such as thermalization. The meaning of thermodynamic variables
associated with the photon gas must not be confused with their classical
counterparts, e.g., the gas temperature cannot be measured by means of standard
thermometers. Although the thermodynamic parameters of a multimode photon gas
result from a rigorous mathematical derivation, their physical meaning is still
unclear. In this work, we report on optical calorimetric measurements, which
exploit nonlinear beam propagation in multimode optical fibers. Our results
show that, indeed, heat only flows from a hot to a cold photon gas subsystem.
This provides an unequivocal demonstration that nonlinear multimode wave
propagation phenomena are governed by the second law of thermodynamics. In
addition to be fundamental, our findings provide a new approach to
light-by-light activated management of laser beams.
