  We numerically determine the entropy for heat-conducting states, which is
connected to the so-called excess heat considered as a basic quantity for
steady-state thermodynamics in nonequilibrium. We adopt an efficient method to
estimate the entropy from the bare heat current and find that the obtained
entropy agrees with the familiar local equilibrium hypothesis well. Our method
possesses a wider applicability than local equilibrium and opens a possibility
to compare thermodynamic properties of complex systems with those in the local
equilibrium. We further investigate the entropy for heat-conducting states and
find that it exhibits both extensive and additive properties; however, the two
properties do not degenerate each other differently from those at equilibrium.
The separation of the extensivity and additivity makes it difficult to apply
powerful thermodynamic methods.
