Relation between power dissipation and imag part of susceptibility

Asked Jul 10 '23 at 20:15

Active Jul 10 '23 at 20:15

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I am trying to understand the following relation between power dissipation and the imaginary part of the susceptibility, from Sethna's Statistical Mechanics textbook. Why does the integral equal the imaginary part of the susceptibility? Also, when doing integration, why can we assume that the bounds are symmetric? Explicit math steps would be greatly appreciated!

asked Jul 10 '23 at 20:15

photonica

I can not open the image link, maybe you could write it down explicitly. This may also help: How imaginary part of susceptibility is measure of dissipation? – Quillo Jul 10 '23 at 21:48
That question doesn't walk through all the math showing how the dissipated power is related to the imag part of susceptibility, so I was still confused – photonica Jul 10 '23 at 22:03
1

How about this one? Fluctuation-dissipation theorem and Kramers-Kronig relations – Quillo Jul 10 '23 at 22:06

Relation between power dissipation and imag part of susceptibility

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