Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar-tensor gravity

Abstract

We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.

More on the first-order thermodynamics of scalar-tensor and Horndeski gravity

“…In order to appreciate the first-order thermodynamics of scalartensor or viable Horndeski gravity [46,47,48,49,50,51,96,66,67,68,95], one should understand what is peculiar to the effective stress-energy tensor of these theories, once their field equations are written as effective Einstein equations. It is not the fact that their effective stress-energy tensor assumes the form of a dissipative fluid-this is true for any symmetric 2-index tensor.…”

First-order thermodynamics of scalar-tensor gravity

“…Since all imperfect fluid quantities vanish, the analogy built in the previous sections becomes trivial: KT is always zero and no approach to equilibrium (or departure from it) be analysed. However, in [13], it was realised that an alternative but equivalent picture of firstorder thermodynamics, based instead on the notion of chemical potential, can address this problem. Although KT vanishes for the fluid describing the minimally coupled scalar, the chemical potential, defined as μ = 2 X does not, and the dissipation to equilibrium can be characterised as φ → const.…”

“…Within this perspective, studying extended theories of gravity helps to understand GR as a special case in a much more general framework, which is a promising way to better understand and eventually overcome its limitations. This is precisely the goal of the approach that we dub "first-order thermodynamics of scalar-tensor gravity", first developed in [8] and extended in [9][10][11][12][13][14][15]. This proposal is based on the observation that the contribution of the scalar field φ to the field equations of scalar-tensor gravity can be described as an effective dissipative fluid, through a simple rewriting of the equations that does not entail extra assumptions [16,17].…”