  Starting from microscopic mechanics, we derive thermodynamic relations for
heat conducting nonequilibrium steady states. The extended Clausius relation
enables one to experimentally determine nonequilibrium entropy to the second
order in the heat current. The associated Shannon-like microscopic expression
of the entropy is suggestive. When the heat current is fixed, the extended
Gibbs relation provides a unified treatment of thermodynamic forces in linear
nonequilibrium regime.
