Continuum and lattice heat currents for oscillator chains.

We show that two commonly used definitions for the heat current give different results-through the Kubo formula-for the heat conductivity of oscillator chains. The difference exists for finite chains, and is expected to be important more generally for small structures. For a chain of N particles that are tethered at the ends, the ratio of the heat conductivities calculated with the two currents differs from unity by O(1/N). For a chain held at constant pressure, the difference from unity decays more slowly, and is consistent with O(1/Neta) with 1>eta>0.5.