Ghost condensate and generalized second law

TL;DR

This paper examines whether the generalized second law of thermodynamics can be violated in ghost condensate models, concluding that in the original scenario, the law holds due to suppressed propagation speed differences and slow energy transfer.

Contribution

It demonstrates that the original ghost condensate scenario does not violate the generalized second law, extending the analysis to gauged ghost condensation.

Findings

Propagation speed differences are suppressed by M^2/M_{Pl}^2.

Energy transfer timescales exceed the Jeans timescale.

The generalized second law remains valid in the original ghost condensate scenario.

Abstract

Dubovsky and Sibiryakov recently proposed a scenario in which particles of different species propagate with different speeds due to their direct couplings to ghost condensate. It was argued that this extended version of ghost condensate allows a gedanken experiment leading to violation of the generalized second law. However, in the original ghost condensate scenario, difference in propagation speeds is suppressed by M^2/M_{Pl}^2, where M is the order parameter of spontaneous Lorentz breaking and M_{Pl} is the Planck scale. In this case the energy transfer necessary for the gedanken experiment is so slow that the timescale of decrease of entropy, if any, is always longer than the Jeans timescale of ghost condensate. Hence the generalized second law is not violated by the gedanken experiment in the original ghost condensate scenario. This conclusion trivially extends to gauged ghost condensation by taking into account accretion of gauged ghost condensate into a black hole.