Zero-viscosity limit in a holographic Gauss–Bonnet liquid

In recent papers, it was hypothesized that there exist dissipationless quantum liquids, i.e., liquids with zero or vanishingly small viscosity and zero entropy production, which nevertheless have nontrivial second-order transport coefficients. A natural candidate for a dissipationless liquid is the hypothetical conformal quantum liquid, whose holographically dual description in the infrared limit is given by the five-dimensional Gauss–Bonnet gravity. It is known that shear viscosity in that theory can be made arbitrarily small as the Gauss–Bonnet coupling parameter approaches a critical value. We evaluate the transport coefficients of a Gauss–Bonnet liquid (nonperturbatively in the coupling parameter; three of the six coefficients were previously unknown) and consider the zero-viscosity limit. We show that three of the five second-order coefficients are nonzero in this limit, but they do not satisfy the criterion of zero entropy production. Hence, the holographic Gauss–Bonnet liquid is not a dissipationless quantum liquid.