Questions tagged [fluctuation-dissipation]
The fluctuation-dissipation tag has no usage guidance.
69
questions
2
votes
1
answer
42
views
Onsager's hypothesis: why is true that correlations decay with increasing time?
I am studying from Chandler's book (Introduction to Modern Statistical Mechanics) the fluctuation-dissipation theorem. Before introducing it, the book states something without really demonstrating it. ...
1
vote
1
answer
52
views
Deriving black body law from fluctuation-dissipation theorem?
Is it possible to prove the Blackbody radiation law using the fluctuation-dissipation theorem?
Has it been done, or is there some reason why it wouldn't work? I would appreciate if you could point me ...
- 258
1
vote
1
answer
58
views
Heat capacity in statistical mechanics
A known result from statistical mechanics is the following fluctuation-dissipation relation:
\begin{equation}
\frac{\partial^2S}{\partial E^2} = - \frac{1}{C_v T^2} \tag{1}
\end{equation}
where $C_v$ ...
1
vote
0
answers
37
views
Clarification regarding Kubo formula and fluctuation-dissipation theorem
In the Wikipedia article for Fluctuation-dissipation theorem, under the section for the derivation in the quantum case, the Kubo formula is quoted.
\begin{align*}
\chi(t-t') = \frac{i}{\hbar} \theta(t ...
- 628
0
votes
1
answer
52
views
Intuition about non-equilibrium Green functions
In the following paper by Fotso and Freericks, the definitions of the Green functions are given as
\begin{align}
G^<(t,t') &= i \langle c^\dagger(t') c(t) \rangle \\
G^R(t,t') &= -i \theta(...
- 628
1
vote
1
answer
58
views
Is there a fermionic fluctuation-dissipation theorem?
Question: is there any fermionic version of fermionic fluctuation–dissipation theorem?
Context:
In classical physics, the fluctuation–dissipation theorem is roughly written as
$$\langle x(t)x(t')\...
- 2,780
3
votes
1
answer
79
views
Consistency of Lindblad-type operator evolution equations
One frequently comes across Lindblad-type operator evolution equations in the Heisenberg picture of the form
$$
\frac{\mathrm{d}}{\mathrm{d}t} A =\mathcal{L}^{\dagger}(A),
$$
where the adjoint ...
- 33
0
votes
0
answers
17
views
Thermal noise in suspensions of mesoscopic particles
By considering the steady state mean-squared-displacement of a particle undergoing Langevin dynamics in a harmonic potential well, Einstein was able to relate the diffusion constant of a colloidal ...
- 2,863
0
votes
2
answers
113
views
Autocorrelation and variance: can the fluctuation-dissipation theorem actually be written in terms of fluctuations?
I am considering the theorem in a statistical mechanics context, but I suppose the question could be extended to other fields where it applies as well.
If we have a system with property $A$ and apply ...
- 862
2
votes
0
answers
73
views
Does the fluctuation-dissipation (FD) relation $\sigma_E^2=k_BT^2C_V$ arise as a special case of the FD theorem?
The classical fluctuation-dissipation theorem states that the power spectral density $S_{\eta\eta}(\omega)$ of a classical random variable $\eta(t)$ is given by $$S_{\eta\eta}(\omega)=\frac{2k_BT}{\...
- 23.9k
34
votes
16
answers
11k
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 ...
- 2,340
1
vote
0
answers
51
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 ...
- 2,195
1
vote
0
answers
42
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-...
- 558
0
votes
1
answer
269
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 ...
- 103
1
vote
1
answer
193
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 ...
- 869
0
votes
1
answer
89
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 ...
- 1,034
0
votes
0
answers
41
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: ...
- 1
5
votes
2
answers
176
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, ...
- 1,034
1
vote
1
answer
74
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 $$S_{AA^\dagger}(-\omega)=e^{-\beta\hbar\omega}S_{...
- 356
0
votes
0
answers
138
views
Problem in derivation of Smoluchowski Equation
I am trying to derive Smoluchowski equation using Fokker Planck equation. I am following the book ''Non Equilibrium Statistical Mechanics'' by Robert Zwanzig. I am attaching a screenshot of a few ...
- 111
12
votes
2
answers
352
views
Does the fluctuations-dissipation theorem hold in active matter for macroscopic physical quantities?
I am trying to understand how the fluctuation–dissipation theorem applies to active matter.
I simulated a system with active motors which may consume energy from the environment to move and exert ...
- 3,114
1
vote
0
answers
55
views
Where does differntial equation of covariance matrix come from?
Does anyone know where the differential equation of covariance matrix comes from?
$$\frac{dC(t)}{dt}=AC(t)+C(t)A^T+D$$
where $C$ is the covariance matrix, $A$ is the drift matrix, and $D$ is the ...
- 11
5
votes
2
answers
413
views
Fluctuation-dissipation theorem in the Keldysh formalism
In Kamenev's book Field Theory of Non-Equilibrium Systems (he also has lecture notes online here, which contains the relevant statement on pg. 17), he states that the following equation
$$G^K(\epsilon)...
- 860
4
votes
2
answers
1k
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. ...
- 842
1
vote
0
answers
34
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-...
- 395
1
vote
2
answers
279
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 ...
- 395
3
votes
1
answer
64
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 ...
- 96
3
votes
1
answer
100
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 ...
- 111
2
votes
0
answers
299
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 ...
- 2,174
0
votes
2
answers
186
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 ...
- 1,107
0
votes
1
answer
151
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 ...
- 1,083
2
votes
1
answer
125
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-...
- 123
4
votes
2
answers
333
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-...
- 557
1
vote
1
answer
143
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 ...
- 45
0
votes
1
answer
335
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
$$\...
- 545
1
vote
1
answer
204
views
Fluctuation dissipation on a ring?
The integral fluctuation theorem is given by:
$$\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),\...
1
vote
1
answer
220
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 ...
- 1,233
2
votes
0
answers
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 ...
user67800
3
votes
0
answers
92
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 ...
- 305
1
vote
0
answers
41
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 ...
- 3,114
7
votes
1
answer
539
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 ...
- 521
3
votes
1
answer
142
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 ...
- 23.9k
3
votes
0
answers
158
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 ...
- 1,022
1
vote
1
answer
65
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 ...
- 143
3
votes
1
answer
730
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 ...
- 8,454
2
votes
1
answer
654
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 ...
3
votes
0
answers
162
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 ...
- 7,472
8
votes
1
answer
577
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 ...
- 109
2
votes
1
answer
359
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)\...
- 952
3
votes
2
answers
371
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 $...
- 1,398