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Prog. Theor. Phys. Vol. 116 No. 5 (2006) pp. 851-871

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Unification of Cosmology and the Second Law of Thermodynamics

— Proposal for Solving the Cosmological Constant
and Inflation Problems —

Holger B. Nielsen1 and Masao Ninomiya2,*

1Niels Bohr Institute, 17, Blegdamsvej, DK2100 Copenhagen, Denmark
2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

(Received August 7, 2006)

Abstract:

We seek to unify the second law of thermodynamics with other physical laws, or, at least to find a law underlying the second law of thermodynamics. Assuming no fine tuning, using a random Hamiltonian, we argue just from the equations of motion – without the second law – that entropy cannot first increase and then decrease except with the rather strict restriction Slarge ≤Ssmall 1 + Ssmall 2. Here Slarge is the “large" entropy in the intermidiate era, while Ssmall 1 and Ssmall 2 are the entropies at certain times before and after the Slarge era. From this theorem asserting that there can exist no strong maximum for the entropy, we argue that an S1 cyclic time model world could have entropy that varies by at most a factor of two and would not be phenomenologically realistic. With an open ended time axis (-∞, ∞) = R, some law underlying the second law of thermodynamics is needed if the entropy is not maximal (i.e. that heat death having y occurred at the start). We derive such a law behind the second law – or a unification of the second law with other laws – by assigning a probability weight P for finding the world/system in various places in phase space. In such a model, P is almost unified with the rest as P = exp (-2 SIm), with SIm being the imaginary part of the action. We quite naturally derive the second law for practical purposes, a Big Bang with two-sided time directions, and find that there is a need for a Hamiltonian density with a well-defined bottom. Assuming that the cosmological constant is a dynamical variable in the sense that it is counted as on “initial condition", we even solve in our model the cosmological constant problem without using the anthropic principle.


URL : http://ptp.ipap.jp/link?PTP/116/851/
DOI : 10.1143/PTP.116.851


*Also at Okayama Institute for Quantum Physics, Kyoyama-cho 1-9, Okayama 700-0015, Japan.

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