Entropy generation, particle creation, and quantum field theory in a cosmological spacetime: When do number and entropy increase\?

Details Entropy generation, particle creation, and quantum field theory in a cosmological spacetime: When do number and entropy increase\? Entropy generation, particle creation, and quantum field theory in a cosmological spacetime: When do number and entropy increase\?

Jun 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrvd..37.3505k&link_type=abstract

Physical Review D (Particles and Fields), Volume 37, Issue 12, 15 June 1988, pp.3505-3521

Physics

Condensed Matter

Statistical Mechanics

40

Theory Of Quantized Fields, Quantum Statistical Mechanics

Scientific paper

This paper reexamines the statistical quantum field theory of a free, minimally coupled, real scalar field Φ in a statically bounded, classical Friedmann cosmology, where the time-dependent scale factor Ω(t) tends to constant values Ω1 and Ω2 for tt2. The principal objective is to investigate the intuition that ``entropy'' S correlates with average particle number , so that increases in induced by parametric amplification manifest a one-to-one connection with increases in S. The definition of particle number Nk becomes unambiguous for t>t2 and t- is guaranteed generically to be positive only for special initial data which, in a number representation, are characterized by ``random phases'' in the sense that any relative phase for the projection of ρ(t1) into two different number eigenstates is ``random'' or ``unobservable physically,'' and averaged over in a density matrix. More importantly for the notion of entropy, random-phase initial data also guarantee an increase in the spread of P(\{k,Nk\}), so that, e.g., the sum of the variances Δ2N+/-k(t2) exceeds the initial Δ2N+/-k(t1). It is this increasing spread in P, rather than the growth in average numbers per se, which suggests that, for initial data manifesting random phases, SN(t2)>SN(t1), a result established rigorously in the limits of strong and weak particle creation.

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