Journal of Statistical Physics, Vol. 49, Nos. 5/6, 1987. p. 1209-1219.
We consider a liquid-vapor interface in thermal equilibrium. The tangential component of the pressure tensor is supposed to depend explicitly upon the position and the density profile. Under this hypothesis the mechanical definition of surface tension becomes a finite summation of N+1 terms related directly to the local compressibility. When the inhomogeneous compressibility equation is considered, the theory provides a microscopic expression of the surface tension coefficient. A calculation for argon near the critical point is done; the agreement with experiment is satisfactory.