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Questions tagged [fluctuation-dissipation]

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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 ...
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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 ...
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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 ...
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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-...
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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-...
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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 ...
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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 $$\...
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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),\...
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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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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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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 ...
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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 ...
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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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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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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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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 ...
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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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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 ...
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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)\...
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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 ...
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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
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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. ...
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2answers
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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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0answers
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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 ...
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 ...
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0answers
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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 ...
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1answer
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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 ...
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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 ...
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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 $D$ ...
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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}\...
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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
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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 ...
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3answers
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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 ...
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2answers
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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 ...