Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters

Abstract

The exact expression for the entropy current of a fluid in presence of two dimensional gravitational anomalies is given. To make it compatible with the second law of thermodynamics; i.e. positivity of the entropy production rate of a system (which is considered to be fundamental), we find a bound on the sum of the two response parameters (${\bar{C}}_1$ and ${\bar{C}}_2$), in terms of the trace and diffeomorphism anomaly coefficients ($c_w$ and $c_g$). The precise expression, we obtain here, is ${\bar{C}}_1+{\bar{C}}_2\le 4{\pi }^2{c}_w+8{\pi }^2{c}_g$. Interestingly, when the bound is saturated corresponding to a reversible process, the result reproduces earlier findings obtained by either studying field theory on the cone or using the {\it Israel-Hartle-Hawking} boundary condition. Finally, possible physical implications and connections with the existing approaches are addressed.

Comments added, to appear in Phys. Rev. D

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