# Questions tagged [fluctuation-dissipation]

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### Problem in derivation of Smoluchowski Equation

I am trying to derive Smoluchowski equation using Fokker Planck equation. I am following the book ''Non Equilibrium Statistical Mechanics'' by Robert Zwanzig. I am attaching a screenshot of a few ...
1answer
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### Does the fluctuations-dissipation theorem hold in active matter for macroscopic physical quantities?

I am trying to understand how the fluctuation–dissipation theorem applies to active matter. I simulated a system with active motors which may consume energy from the environment to move and exert ...
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### Where does differntial equation of covariance matrix come from?

Does anyone know where the differential equation of covariance matrix comes from? $$\frac{dC(t)}{dt}=AC(t)+C(t)A^T+D$$ where $C$ is the covariance matrix, $A$ is the drift matrix, and $D$ is the ...
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### Why should $\langle xf_r\rangle=0$ but $\langle\dot{x}f_r\rangle\ne 0$?

All the $\langle\rangle$ in this question is the mean value theorem over a large number of experiments. Consider a Brownian particle moving in a liquid with the viscosity $\mu$. The equation of ...
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### Fluctuation-dissipation in a quantum Ising Model

For the classical Ising model, the fluctuation-dissipation theorem tells us that the Magnetic susceptibility is proportional to the variance of the magnetization. Is there an equivalent relation for ...
1answer
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### Is it possible to eliminate Van der Waals interactions?

I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...