We study uncharged Rindler hydrodynamics at second order in the derivative expansion. The equation

of state of the theory is given by a vanishing equilibrium energy density.

We derive relations among the transport coefficients by employing two frameworks. First, by the requirement of having an entropy current with a non-negative divergence, second

by studying the thermal partition function on stationary backgrounds.

The relations derived by these two methods are equivalent.

We verify the results by studying explicit examples in flat and curved space-time geometries.