Questions tagged [fluctuation-dissipation]

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Spectral density of fluctuations (white noise/delta-correlated process)

Let I be the current flowing across some junction as a result of N charge carriers of charge q. And let $\langle I (t) \rangle$ be its average. Assume a particle number distribution such that its ...
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Noise spectral density for waveguide: I don't understand this calculation

In Introduction to Quantum Noise, Measurement and Amplification, on page 64 is computed the power spectral density of noise on a classical waveguide. I am really struggling to understand a step of the ...
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Good references for linear response theory

I am looking for good references for linear response theory. I have seen this https://nptel.ac.in/courses/115/106/115106091/ which looks nice but probably a little long (going into too many details). ...
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Fluctuation for diffusion flux (Fick's law)

I am trying to write the formulation for fluctuation in diffusion flux (Fick's law): $$\vec{j}= - \rho D\vec{\nabla} c$$ Then I describe fluctuation in concentration and density as the following: ...
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Fluctuation dissipation theorem : how to identify the response variable and the force in general?

I fully re-edited my question I have a super basic question. Note that I am just beginning to learn linear response theory. General context: If I consider a linear, time invariant, causal system, ...
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Equivalence of thermodynamic ensembles

It is often argued that thermodynamic ensembles are equivalent in the sense that no matter what ensemble one uses for the calculations, one should end up in the same macroscopic equations of state. ...
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What does stochastic nature of work (quantum scale) really mean?

Fluctuation theorems are (also) concerned with defining work in the non-equilibrium regime. Now I've read that in regimes where Fluctuations become very strong (which I assume are the non-...
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Is entropy change always zero after a quasi-static evolution?

If I am thinking in terms of a idealized, perfect carnot cycle I know that in sum $$\Delta S_{\mathrm{total}} = 0.\tag{1}$$ But that does not mean that there is no entropy generated during the ...
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What does $\delta$ represents in FLUCTUATION-DISSIPATION THEOREM?

i am trying to follow the following tutorial. I keep seeing $\delta$ over functions such as $\delta F(x)=F(x)-\langle F(x)\rangle_t$ (Eq 14.4) in this and in other tutorials and questions here. What ...
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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 ...
279 views

Exact solution for non-linear Fokker-Planck equation

I'm searching for exact (analytical) results for FP equation in 2 variables (such as $x$ and $p$ in 1D) with a steady state. Kramer's like (with force due to confining potential, such as harmonic ...
137 views

Fluctuation-dissipation theorem for velocities

I am given the following problem about fluctuation dissipation theorem: Consider an external force $f(t)= \frac{f_0}{2}(e^{i\omega_0 t}+e^{-i\omega_0 t})$ acting on a particle with momentum $p=mv$ in ...
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How to determine the off-diagonal term of magnetic susceptibility tensor from fluctations?

I have run a Monte Carlo simulation of the classical Heisenberg model (in the future I am planning to add other interaction terms). I would like to extract information about the property of the system ...
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What is the fluctuation-dissipation relation for non-quadratic kinetic energies?

Recently I tried to get in touch with some statistical mechanics. I am completely new to the field and hence many things are unclear to me. Currently, I have a question regarding the dissipation-...
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What causes viscosity of a fluid?

Consider a fluid like water. Intuitively I would say that its viscosity is caused by intermolecular interactions among its molecules. But the Einstein-Smoluchowski relation (and the Fluctuation-...
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Thermodynamics Help - Reading through Landau and Lifshitz

I am reading Landau and Lifshitz and I am confused about two steps in the Fluctuation theory chapter. They occur just before Eqn. 3 in "Fluctuations of the fundamental thermodynamic quantities". Here ...
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Fluctuations of free energy in quantum statistical mechanics

I want to calculate the fluctuation of the mean value of the free energy, $\langle F \rangle$, which I denote as $(\Delta F)^2 = \langle F^2\rangle - \langle F\rangle^2$. Since I have calculated the ...
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Thermal fluctuations in orientation of point particles

I am modeling group of point particles with 6 degrees of freedom each - 3 positional degrees of freedom and 3 orientational degrees of freedom. So, each particle has 3 position coordinates and a unit ...
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Fluctuation-dissipation theorem for the acoustic equation

Recently I discovered a paper by R. Snieder on the extraction of the acoustic Green function from cross-correlations of the acoustic noise. What differs this paper from other papers on the subject, is ...
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Is there an equivalency between fluctuation and effective degrees of freedom?

Is it possible to use the fluctuation-dissipation theorem to introduce a new "fictitious" degree of freedom (d.o.f) for an existing coordinate/d.o.f which fluctuates a lot? Consider a non ...
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How does the fluctuation theorem dissipation function become entropy?

In "The Fluctuation Theorem" by Evans and Searles, they derive the transient fluctuation theorem from Liouville's theorem (pg 1541). Following their notation $\Gamma = (\vec{q}, \vec{p})$, they use ...
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Can we take $\sigma^2_N=\frac{\kappa_T}{\beta V}N^2$ to be an example of the fluctuation-dissipation theorem?

In statistical mechanics, the relation $\sigma^2_E=\langle E^2\rangle-\langle E\rangle^2=k_BT^2C_v$ is interpreted ad one of the examples of fluctuation-dissipation theorem. The fluctuation in energy ...
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Does the Lindblad equation satisfy a fluctuation dissipation relation?

The fluctuation dissipation relation is usually stated in terms of an identity that relates the retarded, advanced and either the Keldysh or time-ordered correlators. This is easily enforced in ...
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DPD weight function

I was wondering about the connection between the weight function of the random force and the conservative force between DPD particles in a standard DPD simulation. Both usually have the form [Groot ...
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Fluctuation-dissipation theorem in QFT

If I understand correctly, the fluctuation-dissipation theorem (fdt) in QFT technically arises because of $\pm i\epsilon$ - infinitesimally small summand in the denominator of spectral representation ...
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Heat capacity and fluctuation-dissipation theorem, meaning of energy fluctuations?

I have read that from the fluctuation-dissipation theorem that the heat capacity is proportional to energy fluctuations (or populations fluctuations). In this context what is the meaning of 'energy ...
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Second law of thermodynamics in linear response theory

I am wondering about the appearance of irreversibility in the response functions or equivalently the correlation functions in a statistical mechanics system. The main principle that I have seen where ...
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alternative derivation of Einstein relation

Is there a derivation of the EinsteināSmoluchowski relation without the assumption of the Boltzmann distribution? Every time I see a derivation, it always assumes the Boltzmann distribution, such as ...