Questions tagged [fluctuation-dissipation]

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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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109 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 ...
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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)...
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77 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 ...
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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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44 views

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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25 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: ...
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43 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_{...
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22 views

Fluctuation-dissipation theorem out of equilibrium

Are there generally accepted formulations of the fluctuation-dissipation theorem out of equilibrium? Background: Fluctuation-Dissipation Theorem in the Keldysh Formalism
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56 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 ...
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280 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 ...
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47 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 ...
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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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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-...
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107 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 ...
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210 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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51 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 ...
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65 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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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 ...
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136 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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98 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 ...
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1answer
102 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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211 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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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),\...
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107 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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137 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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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 ...
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82 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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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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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 ...
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437 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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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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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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143 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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57 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 ...
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1answer
614 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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146 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
326 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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321 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 $...
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1answer
386 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
222 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}+...
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1answer
252 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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1answer
629 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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395 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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2answers
85 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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249 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 ...
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236 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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605 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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617 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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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 ...