Following the proposal of steady state thermodynamics (SST) by Oono and Paniconi, we develop a phenomenological theory for steady nonequilibrium states in systems with heat conduction. We find that there is essentially a unique consistent thermodynamics, and make concrete predictions, i.e, the existence of a new osmotic pressure and a shift in the coexistence temperature. These predictions allow one to test for the quantitative validity of SST by comparing them with experiments. Construction of a statistical mechanics that apply to nonequilibrium states has been a challenging open problem in theoretical physics . But so far it is not known how the desired probability measures for nonequilibrium states look like, or even whether the measures can be written in compact forms . Recalling the history that the conventional thermodynamics was an essential guide when Boltzmann, Gibbs, and others constructed equilibrium statistical mechanics, it may be a good idea to start from the level of thermodynamics. The standard theory of nonequilibrium thermodynamics  is based on local equilibrium hypothesis, which roughly asserts that each small part of a nonequilibrium state can b
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