Abstract: In hydrodynamics derivative expansion, transport coefficients are constrained by the requirement that the divergence of an entropy current be locally non-negative. It is well known for a long time from the second law of thermodynamics but recently, it has been conjectured that "some" of these constraints can also be derived from an equilibrium partition function on a weakly curved back ground, to all orders in derivative expansion. I am going to explain how this conjecture can reproduce the well-known constraints on anomaly induced transport coefficients and thermodynamic transport coefficients.