Mathematics – Logic
Scientific paper
Jan 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phdt........38p&link_type=abstract
Thesis (PH.D.)--BROWN UNIVERSITY, 1993.Source: Dissertation Abstracts International, Volume: 54-10, Section: B, page: 5204.
Mathematics
Logic
Scientific paper
We define a new formula for the nonequilibrium entropy of a classical stochastic field. We then apply it to calculate the entropy of cosmological perturbations, in particular of gravitational waves and density perturbations. The dynamics of the linearized cosmological perturbations can be reduced to the analysis of a single scalar field, which carries all the information about the dynamics of both the gravitational field (metric perturbations)and the matter fields (density perturbations). In an inflationary Universe model the origin of perturbations are vacuum fluctuations of a quantized field. The initial vacuum state evolves into a highly excited squeezed state. Our formalism then permits us to define the entropy of the squeezed state in terms of its Gaussian noise, defined in terms of two -point correlation functions. The particular coarse graining that we choose is decoherence in phases in which (a) the phase correlations between the canonical variables are destroyed and (b) the noise is increased by a large amount (by an exponential of the squeeze factor for the squeezed state). With this choice of coarse graining we show (for the example of density perturbations) that the new classical formula for entropy reduces to the entropy specified in terms of one-particle distribution functions (microcanonical ensemble). The entropy of density perturbations on scales of large structures in the Universe dominates over the entropy in cosmic microwave photons on the same scale, while the total entropy of density perturbations (and also of gravitational waves) is suppressed. This difference can be naturally explained by the nonequilibrium character of the distribution function for density perturbations.
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