Kubo formula for thermopower (Seebeck coefficient)

lyuchn
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I have a long-standing puzzle about the Kubo formula of thermopower S=L_{21}/L_{11}.

The electric conductivity (L_{11}) can be expressed in terms of real time current-current correlations.
Similarly, the heat conductivity can be expressed in terms of real time correlations
of heat currents.

So how to relate thermopower, which measures the electric current driven by a temperature gradient, to some kind of current-current correlation. Here it should be the correlation between heat current and electric current. But how to derive this formula for L_{21}?
Can we simply take the gradient of 1/T as an external force? Why this holds?
 
Did you have a look at Landau Lifshitz? Would be my best guess to find something.
 

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