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What is the relationship between persistence length and timescale?

I have calculated the bending persistence length of a polymer using MD simulations in the nanosecond timescale. The persistence length is long (410 nm) compared to the contour length (40-45 nm). But ...
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Are vibrating strings in string theory perpetual motion?

I have never learned string theory, so please forgive me if my question sounds naive or obvious, but I would like to know and I am most likely wrong. As far as I know, strings vibrate in different ...
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How to calculate the thermal radiations of a seawater ball in the microwave range

I'm seeking for guidance on how to calculate the farfield spectral irradiance of the thermal radiations of an object made of a material with known complex permittivity ($\epsilon_r=\epsilon^{'}_r+j\...
Lionel Chemin's user avatar
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Calcuating Fluctuations in (Thermodynamic) Temperature in Microcanonical Ensemble

The definition of (Thermodynamic) Temperature is indeed possible in microcanonical ensemble through the Gibb's Entropy as shown in this work (1). In this scenario, the temperature, essentially a ...
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Fluctuational Electrodynamics: Ensemble Average

I am trying to understand the ensemble average often stated in the fluctuation-dissipation theorem describing thermal radiation: Here, the overbar denotes the ensemble average. My question is, how is ...
Physics_Student's user avatar
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Time evolution operator with chemical potential

In the Bruus and Flensberg textbook, section 1.5, it is mentioned that Basically, the result obtained from the canonical ensemble is carried over to the grand canonical ensemble by the substitution $...
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Virial theorem for momentum fluctuations

In the paper https://journals.aps.org/pr/abstract/10.1103/PhysRev.109.1464 Lebowitz attempted to derive an estimation of the magnitude of center of mass momentum fluctuations in the presence of ...
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Spontaneous emission as dissipation and fluctuation

Suppose we have some sort of medium and we want to build an effective theory of light inside. Of course we want to calculation the dielectric constant, which in turn is determined by the ...
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Why do statistical physics and thermodynamics care about fluctuations?

Fluctuation seems to be an eternal theme in the study of statistical physics and thermodynamics, why do we need to care about it? Just for stability? Any comments would be appreciated
Moon Traveler's user avatar
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Suscpectibility in Ising networks

I am struggling to find good references on how the susceptibility described phase transitions in Ising networks. First of all i struggle to find a good defintion for the susceptibility. I understood ...
Stijn Van Vooren's user avatar
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A simple picture for work fluctuation relations?

One possible formulation of the second law of thermodynamics is that the work extracted during the change of a thermodynamic system between two thermodynamic states is at most equal to the free energy ...
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Relation between power dissipation and imag part of susceptibility [duplicate]

I am trying to understand the following relation between power dissipation and the imaginary part of the susceptibility, from Sethna's Statistical Mechanics textbook. Why does the integral equal the ...
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Deriving the fluctuation-dissipation theorem

In the derivation of the classical version of the fluctuation-dissipation theorem here, they expand the equilibrium distribution function (with Hamiltonian $H(x) = H_{0}(x) - f_{0}x$) $$ W(x, 0) = \...
nullspace's user avatar
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Wiki video shows that vacuum fluctuations exist, despite that vacuum fluctuations do not exist

I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually ...
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4 votes
1 answer
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Fluctuation-dissipation and lesser Green's function

I learned from a lecture that $G^{<}=-f(\epsilon)(G^r-G^a)$ is a type of fluctuation-dissipation theorem. However as far as I know the fluctuation-dissipation theorem is stated as $S(\omega)=2\hbar(...
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Ito-Stratonovich drift term for spatial white noise

Suppose I have a Langevin equation with multiplicative noise of the form $$ \dot{x} = f(x) + g(x)\eta(t) $$ where $ \eta(t) $ is a Gaussian white noise with zero average, unit strength, and delta ...
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Use equipatition theorem when studying Brownian motion [duplicate]

Not a physicist so excuse my ignorance. I am currently studying introductory topics on Brownian mechanics. Utilizing the Langevin equation for a Brownian particle submerged in a fluid with no external ...
Christos's user avatar
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How to evaluate the integral of velocity autocorrelation function for calculating the diffusion coefficient

I am reading Kubo's review article "The fluctuation-dissipation theorem" (http://www-f1.ijs.si/~ramsak/km1/kubo.pdf) Could someone help me with how Eq. 2.5 is derived? I am confused with how ...
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What is the fractional frequency stability of a thermal damped harmonic oscillator?

Suppose I have a lightly driven (classical) damped harmonic oscillator at temperature $T$. Suppose $\omega$ and $Q$ are specified as well as the mean energy $\bar{E}$ in the oscillator due to the ...
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Does an electron undergo a form of Brownian motion in the vacuum?

There are some questions on StackExchange such as this one Brownian Motion in Vacuum asking about Brownian motion in the vacuum. There are related papers such as this one: https://arxiv.org/abs/quant-...
Andrew Steane's user avatar
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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. ...
Salvatore Manfredi D's user avatar
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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 ...
JustThinking's user avatar
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1 answer
298 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 $C_v$ ...
Emanuele Giordano's user avatar
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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 ...
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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(...
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Is there a fermionic fluctuation-dissipation theorem?

Question: is there any fermionic version of the fluctuation–dissipation theorem? Context: In classical physics, the fluctuation–dissipation theorem is roughly written as $$\langle x(t)x(t')\rangle = 2\...
Mauricio's user avatar
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4 votes
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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 ...
mkay's user avatar
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2 answers
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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 ...
Barbaud Julien's user avatar
3 votes
0 answers
145 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}{\...
SRS's user avatar
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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 ...
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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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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-...
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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 ...
RoyalGoose's user avatar
1 vote
1 answer
302 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 ...
Lopey Tall's user avatar
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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 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: ...
mojijoon's user avatar
6 votes
2 answers
338 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, ...
StarBucK's user avatar
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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_{...
RicardoP's user avatar
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1 answer
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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 ...
Mitradip Das's user avatar
12 votes
2 answers
475 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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1 vote
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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 ...
Ghaem's user avatar
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7 votes
2 answers
937 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)...
Henry Shackleton's user avatar
6 votes
2 answers
2k 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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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-...
CatoMaths's user avatar
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2 votes
2 answers
488 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 ...
CatoMaths's user avatar
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3 votes
1 answer
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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 ...
havakok's user avatar
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4 votes
1 answer
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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 ...
noisyoscillator's user avatar
2 votes
0 answers
328 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 ...
Alexander's user avatar
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2 answers
298 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 ...
Mathphys meister's user avatar
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1 answer
219 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 ...
skdys's user avatar
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