  We investigate the effective temperature of a harmonic chain whose two ends
are coupled to two baths at different temperatures. We propose to take the
weighted average temperature as the effective temperature of the system. The
weight factors are related to the couplings between the system and two baths as
well as the asymmetry of interactions between oscillators. We revisit the
thermodynamics of nonequilibrium steady states based on the weighted average
temperature. It is found that the fundamental thermodynamic relations in
nonequilibrium steady states possess similar concise forms as those in
equilibrium thermodynamics, provided that we replace the temperature in
equilibrium with the weighted average temperature in steady states. We also
illustrate the procedure to calculate the effective temperatures via four
examples.
