Two-dimensional quantum cosmology: Directions of dynamical and thermodynamic arrows of time

Takeshi Fukuyama and Masahiro Morikawa
Phys. Rev. D 39, 462 – Published 15 January 1989
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Abstract

Two-dimensional quantum cosmology is studied to clarify the issue associated with the arrow of time. We introduce a density-matrix description for the minisuperspace by projecting out nonzero modes of the wave function of the whole Universe. Thermodynamic time is determined by the direction in which the quantum coherence of minisuperspace variables decreases. This arrow of time is compared with that of dynamical time which is determined by the semiclassical approximation for the density matrix. We reconfirm that the global time cannot properly be defined for the thermodynamic times as well as for the dynamical time in a closed universe. The arrows of dynamical and thermodynamic times coincide with the cosmological arrow of time.

  • Received 9 August 1988

DOI:https://doi.org/10.1103/PhysRevD.39.462

©1989 American Physical Society

Authors & Affiliations

Takeshi Fukuyama

  • Department of Physics, Ritsumeikan University, Kyoto 603, Japan

Masahiro Morikawa

  • Department of Physics, Kyoto University, Kyoto 606, Japan

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Vol. 39, Iss. 2 — 15 January 1989

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