# Can one formulate a fluctuation-dissipation theorem in presence of non-Gaussian noise sources?

The fluctuation dissipation theorem relates the linear response of a system to Gaussian fluctuations. The natural question that comes to my mind is the possible derivation of an analogous FDT in presence of non-Gaussian noise. I would like to know if such an attempt has already been made with links to relevant literature. If not, then what are the difficulties (conceptual or technical) towards such a derivation?

You might be interested in the nonlinear fluctuation dissipation theorem. Here are some sources:

EDIT: Here are some possibly more relevant references for you on a linear system driven by non-Gaussian noise:

A paper by Kanazawa et. al.

A presentation by Kanazawa

A paper by Dubkov et. al.

A paper by Field et. al.

A proof by Grafov

• Thanks for the references. I will take a look at them. I do have the Kubo's two volume book and it's a great reference. I just wanted some clarification on FDTs for linear Langevin systems driven by non-Gaussian noise. Would appreciate any comments on that. I am not explicitly asking about non-linearity in responses here. – noisyoscillator Dec 31 '18 at 14:42
• @noisyoscillator Added a few additional references that might be more what you're looking for. – Joshuah Heath Dec 31 '18 at 16:31
• Thanks a lot Joshuah. These latest additions are more in line with what I was looking for. I was going through Kanazawa's work and his Springer thesis while you posted the links. I appreciate your help in this regard. Cheers and a happy new year! – noisyoscillator Dec 31 '18 at 19:33
• Still it looks like a general FDR for linear systems driven by non-Gaussian sources is missing. I found a paper discussing an FDR when the system is driven by Lévy type noise. – noisyoscillator Dec 31 '18 at 19:59