We generalize a previous version of nonequilibrium entropy for viscous heat conducting fluids by including a new term of third order in the dissipative fluxes. This new term is seen to be related to equilibrium third moments and nonequilibrium second moments of fluctuations of the heat flux and the viscous pressure tensor, and to the relaxation matrix of nonequilibrium fluctuations. We also discuss the most convenient formulation of the second law in the presence of third-order terms. The positiveness of the total entropy production leads to results beyond the scope of the formulation based on the positiveness of just the second-order entropy production. © 1983 Walter de Gruyter. All rights reserved.