I show that the usual definitions of entropy and degree of polarization are not relevant for nonlinear optical waves, because they would lead to the erroneous conclusion that a genuine process of reversible propagation would be characterized by an irreversible process of entropy production. To circumvent this problem, I propose appropriate definitions of entropy and degree of polarization that depend on all the statistical moments of the nonlinear wave, so that they exhibit the satisfactory property to be conserved during a reversible propagation process.
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