Questions tagged [fluctuation-dissipation]
The fluctuation-dissipation tag has no usage guidance.
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1answer
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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 ...
3
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1answer
27 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
245 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 ...
1
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2answers
79 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
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1answer
23 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
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1answer
72 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
132 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-...
1
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1answer
69 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
105 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
$$\...
1
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1answer
156 views
Fluctuation dissipation on a ring?
The integral fluctuation theorem is given by:
$$\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
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1answer
67 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 ...
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0answers
39 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 ...
2
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0answers
49 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
30 views
Trouble in understanding the formula for drift current in Stokes-Einstein relation
In the derivation Stokes-Einstein relation, which relates diffusion and damping, we basically use the fact that diffusion current and drift current must balance each other at equilibrium.
But I have ...
1
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0answers
35 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 ...
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1answer
254 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 ...
4
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1answer
76 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
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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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0answers
113 views
Is creating ONLY a matter (without antimatter) from vacuum physically possible?
We all know that the vacuum fluctuates, creating a pairs of matter-antimatter particles. This is probably even scientifically proven. Is physics allows for a situation where the fluctuations of the ...
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0answers
53 views
Can Fluctuation-Dissipation Theorem Apply to Magnetic Forces in Multi-Spin Systems
Let's say I have multiple spin systems (atoms in a protein) in a solution of water and the spin systems are all producing a magnetic field $\mathrm{B_{loc}}$ that affects nearby spin systems.
Will the ...
1
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1answer
47 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
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1answer
432 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 ...
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0answers
307 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 ...
2
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0answers
127 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 ...
2
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1answer
261 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)\...
2
votes
2answers
249 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
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1answer
307 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 ...
1
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1answer
154 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
votes
1answer
468 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 ...
5
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1answer
318 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
2k 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
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2answers
77 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
176 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
211 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 ...
2
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0answers
203 views
Fluctuation Dissipation Theorem [closed]
I take this course at university called Waves and Optics, and a few lectures ago our teacher talked about the Fluctuation Dissipation theorem but I didn't really understand it. The math behind it is a ...
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2answers
551 views
Nonequilibrium thermodynamics in a Boltzmann picture
The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so ...
4
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1answer
217 views
Quantum fluctuations in a classical domain?
"In the presence of chaos, even small fluctuations
(including quantum fluctuations) can be amplified to produce large uncertainties in later
behavior"(http://arxiv.org/pdf/gr-qc/9210010v2.pdf)
Is there ...
1
vote
1answer
339 views
Stokes-Einstein's formula results in incorrect units for rotational drag coefficient
The Stokes-Einstein-Sutherland relationship,
$$D = \frac{kT}{ 6 \pi \eta a}$$
where $D$ is the translational diffusivity is well known. A similar relationship is used to calculate the rotational ...
2
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2answers
653 views
Error in variance
I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
2
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1answer
352 views
Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation
Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
5
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2answers
549 views
Question about thermodynamic conjugate quantities
I've come across the Onsager reciprocal principle. It's almost clear, except for thermodynamic conjugate quantities - what's that, physical meaning (except the formal definitions: $X_i = -\frac{1}{k}\...
4
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4answers
712 views
Friction at zero temperature?
By the fluctuation-dissipation theorem (detailed-balance for Langevin equation), $$\sigma^2 = 2 \gamma k_B T$$ where $\sigma$ is the variance of noise, $\gamma$ is a friction coefficient, $k_B$ is ...
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3answers
1k views
How to include random force in the simulation (Classical Molecular Dynamics)
I need to implement a random force in my code according to the fluctuation dissipation theorem. I have a Gaussian distribution function ready width average 0 and distribution 1 and I know I need to ...
5
votes
3answers
1k views
What happens if you connect a hot resistor to a cold resistor?
Kind of an extension to this question:
If you heat up an object, and put it in contact with a colder object, in an ideal insulated box, the heat from one will transfer to the other through thermal ...
10
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2answers
1k views
Quantum shot-noise and the fluctuation dissipation theorem
Classically, shot noise observed in the signal generated by a laser incident on a photodiode is explained as being due to the quantization of light into photons, giving rise to a Poisson process. In ...
