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Constraints on the second order transport coefficients of an uncharged fluid

In this note we have tried to determine how the existence of a local entropy current with non-negative divergence constrains the second order transport coefficients of an uncharged fluid, following the procedure described in \cite{Romatschke:2009kr}. Just on symmetry ground the stress tensor of an uncharged fluid can have 15 transport coefficients at second order in derivative expansion. The condition of entropy-increase gives five relations among these 15 coefficients. So finally the relativistic stress tensor of an uncharged fluid can have 10 independent transport coefficients at second order.