de Sitter thermodynamics in the canonical ensemble - General Relativity and Quantum CosmologyReport as inadecuate

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Abstract: The existing thermodynamics of the cosmological horizon in de-Sitterspacetime is established in the micro-canonical ensemble, while thermodynamicsof black hole horizons are established in the canonical ensemble. Generally inthe ordinary thermodynamics and statistical mechanics, both of themicro-canonical and canonical ensembles yield the same equation of state forany thermodynamic system. This implies the existence of a formulation ofde-Sitter thermodynamics based on the canonical ensemble. This paper reproducesthe de-Sitter thermodynamics in the canonical ensemble. The procedure is asfollows: We put a spherical wall at the center of de-Sitter spacetime, whosemass is negligible and perfectly reflects the Hawking radiation coming from thecosmological horizon. Then the region enclosed by the wall and horizon settlesdown to a thermal equilibrium state, for which the Euclidean action isevaluated and the partition function is obtained. The integration constantsubtraction term of Euclidean action is determined to reproduce the equationof state e.g. entropy-area law verified already in the micro-canonicalensemble. Our de-Sitter canonical ensemble is well-defined to preserve the-thermodynamic consistency-, which means that the state variables satisfy notonly the four laws of thermodynamics but also the appropriate differentialrelations with thermodynamic functions; e.g. partial derivatives of the freeenergy give the entropy, pressure, and so on. The special role of cosmologicalconstant in de-Sitter thermodynamics is also revealed.

Author: Hiromi Saida


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