Nonequilibrium thermodynamics for open systems

We develop the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework of nonequilibrium thermodynamics for open systems. A clear distinction between bulk and boundary contributions to the Poisson and dissipative brackets employed to generate reversible and irreversible contributions to time evolution from energy and entropy allows us to formulate the bulk equations as well as the exchange and interaction with the environment directly. The full brackets keep all the structure and hence the predictive power of the original GENERIC for isolated systems. The straightforward procedure is illustrated for hydrodynamics of open systems. Boltzmann's kinetic equation is discussed as a further example. In the Appendix, the thermodynamic treatment of surface excess variables at walls and their role in boundary conditions for the bulk variables is exemplified for a diffusion cell.