Questions tagged [fluctuation-dissipation]
The fluctuation-dissipation tag has no usage guidance.
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questions
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Does the fluctuation-dissipation (FD) relation $\sigma_E^2=k_BT^2C_V$ arise as a special case of the FD theorem?
The classical fluctuation-dissipation theorem states that the power spectral density $S_{\eta\eta}(\omega)$ of a classical random variable $\eta(t)$ is given by $$S_{\eta\eta}(\omega)=\frac{2k_BT}{\...
33
votes
15answers
10k views
Can a broken egg spontaneously reassemble itself (as in the video)?
According to the fluctuation theorem, the second law of thermodynamics is a statistical law. Violations at the micro scale, therefore, certainly have a non-zero probability. However, the application ...
0
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0answers
43 views
Computational detail in derivation of Green-Kubo relation for diffusion coefficient
I read Kubos paper on the Fluctuation Dissipation Theorem
https://www.mrc-lmb.cam.ac.uk/genomes/madanm/balaji/kubo.pdf
and right at the beginning there is a calculation which seems a bit miraculous to ...
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0answers
49 views
How to derive the response function of $m\ddot x + \gamma \dot x + kx = f$?
In a lecture on fluctuation-dissipation theorem, it is stated that
EOM: $m\ddot x + \gamma \dot x + kx = f$
Response function $\chi(\omega) = (-m \omega^2 + i\gamma \omega +
> k)^{-1}$
However, I ...
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0answers
34 views
Fluctuation-Dissipation Relation for Quantum Phase Transitions
I am looking for a formulation for the fluctuation-dissipation relation connecting the correlation related quantities with the thermodynamic functions at the quantum critical point.
The fluctuation-...
0
votes
1answer
82 views
Is it possible to use fluid dynamics to trade in the financial market?
I read somewhere that there is an investment fund in the USA which in its trading decisions uses physical laws of hydrodynamics. I asked my physicist friend, on the account of what is really in ...
1
vote
1answer
136 views
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 ...
0
votes
1answer
83 views
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 ...
0
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0answers
28 views
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 $$
Then I describe fluctuation in concentration and density as the following: ...
5
votes
2answers
123 views
Fluctuation dissipation theorem : how to identify the response variable and the force in general?
I fully re-edited my question
I have a super basic question. Note that I am just beginning to learn linear response theory.
General context:
If I consider a linear, time invariant, causal system, ...
1
vote
1answer
59 views
The fluctuation-dissipation theorem
In Giuliani & Vignale's Quantum Theory of the Electron Liquid, in page 126, they point out that the absorption and emission spectra are related by $$S_{AA^\dagger}(-\omega)=e^{-\beta\hbar\omega}S_{...
0
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0answers
90 views
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 ...
12
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1answer
306 views
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 ...
1
vote
0answers
51 views
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 ...
4
votes
2answers
242 views
Fluctuation-Dissipation Theorem in the Keldysh Formalism
In Kamenev's book Field Theory of Non-Equilibrium Systems (he also has lecture notes online here, which contains the relevant statement on pg. 17), he states that the following equation
$$G^K(\epsilon)...
3
votes
2answers
666 views
Equivalence of thermodynamic ensembles
It is often argued that thermodynamic ensembles are equivalent in the sense that no matter what ensemble one uses for the calculations, one should end up in the same macroscopic equations of state. ...
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0answers
33 views
What does stochastic nature of work (quantum scale) really mean?
Fluctuation theorems are (also) concerned with defining work in the non-equilibrium regime.
Now I've read that in regimes where Fluctuations become very strong (which I assume are the non-...
1
vote
2answers
188 views
Is entropy change always zero after a quasi-static evolution?
If I am thinking in terms of a idealized, perfect carnot cycle I know that in sum
$$\Delta S_{\mathrm{total}} = 0.\tag{1}$$
But that does not mean that there is no entropy generated during the ...
3
votes
1answer
57 views
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 ...
3
votes
1answer
81 views
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 ...
2
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0answers
285 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 ...
0
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2answers
152 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 ...
0
votes
1answer
118 views
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 ...
2
votes
1answer
114 views
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-...
4
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2answers
246 views
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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1answer
122 views
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 ...
0
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1answer
251 views
Fluctuations in Fluctuation Dissipation theorem
In the derivation of the Fluctuation-Dissipation theorem. We encounter an identity
$$ \langle\delta A(t) \delta B(0) \rangle = \langle A(t)B(0)\rangle-\langle A \rangle\langle B\rangle$$
where
$$\...
1
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1answer
176 views
Fluctuation dissipation on a ring?
The integral fluctuation theorem is given by:
$$\left< e^{-R}\right>=1\tag{0}$$
where:
$$R\equiv \ln \left( \frac{p_0(\vec n_0) p[\vec n(\tau),\vec c(\tau)]}{p_f(\vec n) \cdot p[\tilde n(\tau),\...
asked Feb 2 '18 at 19:48
Quantum spaghettification
6,3627 gold badges44 silver badges120 bronze badges
1
vote
1answer
165 views
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 ...
2
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0answers
40 views
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 ...
3
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0answers
87 views
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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0answers
38 views
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 ...
7
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1answer
465 views
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 ...
3
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1answer
109 views
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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0answers
146 views
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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vote
1answer
62 views
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 ...
3
votes
1answer
666 views
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 ...
2
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1answer
554 views
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 ...
asked Apr 16 '16 at 4:42
Quantum spaghettification
6,3627 gold badges44 silver badges120 bronze badges
3
votes
0answers
154 views
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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1answer
452 views
Fluctuation-dissipation theorem and Kramers-Kronig relations
Is there any connection between fluctuation dissipation theorem and Kramers-Kronig relations? They are often described together under linear response theory but I do not see any exact connection (like ...
2
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1answer
341 views
Massless brownian particle Langevin equation and FDT
Given the Langevin equation of a massless brownian particle:
$$
\gamma \dot{x}=\eta,
$$
where $\gamma$ is the friction coefficent and $\eta$ the noise ($\langle\eta \rangle =0$ and $\langle\eta(t)\...
3
votes
2answers
342 views
how to simulate a steep potential barrier in langevin equation
When simulating a Langevin equation, how is a vertical potential barrier handled?
I have the time overdamped evolution of the position $x$, described by
$\gamma\frac{dx}{dt}=-V'(x)+\eta(t)$
where $...
2
votes
1answer
395 views
alternative derivation of Einstein relation
Is there a derivation of the Einstein–Smoluchowski relation without the assumption of the Boltzmann distribution? Every time I see a derivation, it always assumes the Boltzmann distribution, such as ...
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1answer
234 views
Confused by Langevin Equation
Trying to understand the Langevin Equation. In particular, this passage from a Wikipedia article has me confused (section: "Thermal Noise in an Electrical Resistor"):
$\frac{dU}{dt} =-\frac{U}{RC}+...
2
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1answer
666 views
Drag force acting on a disk in a 2D system
I have a 2-dimensional system with behavior governed by Langevin dynamics in which disks (circles) move through a fluid. In the Langevin equation, there is a velocity-dependent term that accounts for ...
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1answer
416 views
Does the skin effect, eddy current / hysteresis losses contribute to Johnson noise in an inductor?
Based on my very basic understanding of the Johnson noise, it's not just a DC phenomena, but should change with frequency in a system, where there is a frequency dependent, real component to the ...
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3answers
4k views
What information is contained in the quantum spectral density?
Consider a harmonic oscillator system with Hamiltonian
$$\hat{H} = \frac{1}{2} A \hat{u}^2 + \frac{1}{2} B \hat{v}^2 \qquad
[\hat{u}, \hat{v}]=i \gamma $$
where $A$, $B$, and $\gamma$ are all real.
...
2
votes
2answers
89 views
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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0answers
259 views
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 ...
3
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1answer
258 views
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 ...
