Entropy of a Classical Stochastic Field and Cosmological Perturbation

We propose a general definition of nonequilibrium entropy of a classical stochastic field. As an example of particular interest in cosmology we apply this definition to compute the entropy of density perturbations in an inflationary Universe. On the scales of structures in the Universe, the entropy of density perturbations dominates over the statistical fluctuations of the entropy of cosmic microwave photons, indicating the relevance of the entropy of density fluctuations for structure formation.