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Actually, there are 2 questions.

The first one is how to understand the dissipation function used in the fluctuation dissipation theory. I notice that for a dielectric material with a complex dielectric function, this dissipation function will be the imaginary part of the dielectric function. Does this imply that we need to trace the absorption process and finally get the correct dissipation function in a thermal equilibrium situation?

The second question is, does this dielectric function used here consider the effect of environment? We know that we can modify the photonic environment and further modify the absorption and emission process. One typical example is the modification of the local density of states. Once this LDOS is modified, do we need to define an effective dissipation function here? For example, if the LDOS is enlarged for 10 times and we assume the occupation number is always the maximum, this means in equilibrium the absorption will also be enlarged for 10 times. Now, shall we consider an effective dissipation function which will be 10*Im{eps} now?

Thanks for the discussion.