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Questions tagged [non-equilibrium]

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What is the intuition behind the statement that non-equilibrium systems with static disorder are self-averaging?

In this paper by C. De Dominics, he makes the argument that in a dynamical statistical mechanics system, one doesn't need to apply the replica trick and can directly disorder average the generating ...
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20 views

Detailed Balance Violation and Fokker-Planck Equation

Suppose I have a system with N sites, and each site can be modified (M) or anti-modified (A). Transitions between these two states are in part random, and in part auto-regulated by recruitment of At ...
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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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1answer
154 views

Heat transfer between a common material and a non-thermalizable one?

I've read that some systems cannot reach equilibrium (page 15 of the book Selected Scientific Papers of Sir Rudolf Peierls: With Commentary or R. Peierls, “Zur kinetischen Theorie der Wärmeleitung in ...
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Why the distribution of Fluctuationg force in brownian motion has gaussian distribution?

I am reading the Zwanzig's book and I have a confusion about the average of the fluctuating force and its distribution. As it says $F(t)$ is a random variable that means it has a probability ...
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51 views

Statistical physics at very large particle number

According to this manuscript http://www.math.lmu.de/~michel/credits/Federica_Pezzotti_phd.pdf it is proposed (e.g. at page 18) that particle correlations between particles can be neglected in the ...
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Why are the electrodes in thermodynamic equilibrium for a working solar cell?

I was reading a paper that performed simulation of a solar cell under illuminated conditions. Obviously, in these conditions, the device is out of thermodynamic equilibrium. For example the ...
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Is there a multiscale analysis for field theories?

Consider a (zero dimensional) Gaussian field theory described by the dynamical action $$S = \int_t \tilde{\phi}(t) \left[\partial_t \phi(t) + M(t) \phi(t)\right] - \gamma \tilde{\phi}(t)^2\, .$$ $\...
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51 views

What is the difference between non-equilibrium and equilibrium phase transitions?

My question is about the distinction between certain kinds of phase transitions. I understand what the difference between first and second order ones are. What is the difference between non ...
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1answer
38 views

Why does the Boltzmann equation deal with single-particle phase space density?

Why does the Boltzmann equation deal with single-particle phase space density $\rho_{1}(\textbf{r}_1,\textbf{p}_1,t)$ rather than the N-particle phase space density $\rho(\{\textbf{r}_i,\textbf{p}_i,t\...
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Book(s) fills the gap from introductory thermo to nonequilibrium thermo/stat mech for self-taught student?

I know this is a big question. But as a graduate student, my research is somehow related to nonequilibrium thermodynamics/statistical mechanics. TBH, I hate how some research treat this subject like a ...
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Do electrons really diffuse when a temperature gradient is applied?

In many websites and books, it is generally said that the charge carriers, be it electrons or holes, diffuse through the considered material when a temperature gradient is applied. However I have ...
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56 views

How to numerically calculate Fisher zeros?

The main quantity in the study of dynamical quantum phase transition (DQPT) is Loschmidt echo amplitude defined as $G(t)=\langle \Psi_{0}|\Psi_{0}(t)\rangle=\langle \Psi_{0}|e^{-iHt}|\Psi_{0}\rangle$...
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1answer
47 views

Work performed by ramping of magnetic field (non-interacting Ising model) [closed]

Consider the following hamiltonian $$H=-h\sum_{i=1}^N\sigma_i$$ where $\sigma_i=\pm1$ and $h$ is the magnetization. Let us assume that the system is equilibrated with a bath at temperature $T$ with ...
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78 views

Does Irreversibly/no detailed balance implies there is no thermal equilibrium?

Consider the following transition matrix $$ T= \left[ {\begin{array}{cccc} \frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6}\\ \frac{1}{3} & \frac{1}{4} & \frac{1}{...
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Cahn-Hilliard free energy, additional term in the writing of the thermodynamical relationship

If we write the free energy like Cahn-Hilliard : $f'=f+\frac{\epsilon^2}{2}(\nabla \phi)^2$, with the primed symbol as the value for the non uniform system and the non-primed symbols for the uniform ...
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35 views

free stress boundary condition

I would like to understand better the free stress boundary condition. Indeed, force equilibrium writes $\nabla.\sigma=0$, and not $\sigma=0$, so which basic physical principle (such as force ...
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Closed form of Iterated integrals arising in Fredholm's integral equation solution in the context of Nonequilibrium Quantum field Theory?

While solving a Non-equilibrium quantum field theory problem I came across this class of $2n_{}^{\text{th}}$ order iterated integral : $$F(T_{}^{},T_{0}^{},\epsilon)=\int_{T_{0}^{}}^{T_{}^{}}dt_{1}^{}...
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What sense is there in entropy arguments when the system can't be known to be ergodic?

What sense does "entropy" make in non-equilibrium dynamics? What is its definition? How is the "entropy of the early universe" calculated, for example? And how can the "entropy of the universe" be ...
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Generalized reaction rate for elementary process

Most textbooks give the reaction rate $$r = k [\mathrm{R}_1]^{a_1}[\mathrm{R}_2]^{a_2} \tag{1}$$ for the elementary process $a_1 \mathrm{R}_1 + a_2 \mathrm{R}_2 \rightarrow \mathrm{P}$. However, ...
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1answer
53 views

How is 'nonlinear optics' related to 'nonequilibrium'?

According to what I found, nonlinear optical process is related to nonequilibrium physics - nonequilibrium green's function (Keldysh green's function/formalism) appears in nonlinear optics. However, ...
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1answer
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Formation of patterns in instabilities according to the wavelength of instability

Do the wavelengths of the instability have an influence on the type of patterns that we are going to get? Meaning for example in 2D, if the unstable wavelengths are small with respect to the size of ...
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Derivation of the Keldysh-Non-Linear-Sigma model

I have to give a presentation on the Keldysh Non Linear Sigma model in a proseminar at my university. I am new to the topic and I have had some problems with understanding the literature. My main ...
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Why is a quantum quench considered as a quantum analog of a thermodynamic transformation?

In the paper of A. Silva, he mentioned that it is possible to characterize a quantum quench, from the perspective of nonequilibrium physics, using work statistics because the quantum quench is ...
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47 views

What is meant by “phase space structure”?

I've heard that non-equilibrium systems have the property that their phase space has a structure, as opposed to 'structure-less' phases spaces of equilibrium systems. What does this precisely mean? I'...
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How to define a generalised Gibbs ensemble (GGE) for classical integrable systems?

We have developed a complete description of generalised Gibbs ensemble (GGE) for quantum integrable systems, after including quasi-local charges. However, for classical integrable systems, such ...
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1answer
56 views

Kramers Equation and Ito vs Stratonovich

In the derivation of the (Klein)-Kramers equation it is possible to start from the differential equations: $$\frac{d\vec v(t)}{dt}=\vec F(\vec r)-\zeta(\vec r) \vec v(t)+\sqrt{2\zeta(\vec r)k_B T(\vec ...
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1answer
17 views

Rotational diffusion - why isn't $\hat n(t)=\hat n(0) \; \forall t$?

Consider the rotational Langevin equation in the absence of an external force: $$\frac{d \hat n(t)}{dt} =\vec{\xi}(t) \times \hat n(t)$$ where $\vec \xi(t)$ is a Gaussian white noise and $\hat n(t) \...
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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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What is the relation between eigenstate thermalisation and infinite heating in Floquet systems?

Closed quantum systems with periodically changing parameters (Floquet systems) typically heat up to an infinite temperature at large times. I have read multiple times (the last time was here) that ...
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30 views

Logistic Growth: Mean Field Equation

I was told a while ago that for the logistics growth process: $$x \underset{k_2}{\stackrel{k_1}{\rightleftharpoons}}x+x$$the mean field equation for the population $n$ is given by: $$\frac{d\bar n}{dt}...
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1answer
68 views

Why is it interesting to study “quantum quench” at a critical point?

In the presentation, "Quantum Quenches in Extended Systems", by S. Sotiriadis, P. Calabrese and J. Cardy, it was pointed out that quatum quench through a critical point remains an open problem. Why ...
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1answer
189 views

How to pass for Langevin equation to Fokker-Planck equation?

What is the procedure to pass from the description of a phenomenon made by the Langevin equation: $$ \frac{dv}{dt}=-\frac{v}{\tau}+\sqrt{2c}\,\eta $$ to the corresponding description with the Fokker-...
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1answer
49 views

Why is matter wave field usually assumed to be be intrinsically stable?

In the paper "Collapse and revival of the matter wave field of a Bose-Einstein condensate" by M. Greiner, O. Mandel, T. Haensch and I. Bloch, it was stated that Bose-Einstein condensate (BEC) ...
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1answer
40 views

Uniqueness of the square-root of the diffusion matrix?

In the Langevin equation with hydrodynamic interactions the stochastic force on particle $a$ is: $$ \sqrt{2k_BT} A^{ab}_{ij} \xi^{b}_j(t)$$ where $\xi$ is a unit white noise. Here $ A^{ab}_{ij} $ is ...
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Relationship between Keldysh formalism and time-dependent perturbation theory

When treating systems in weak external time-dependent electromagnetic field we can use usual time-dependent perturbation theory or the Keldysh formalism which is tailored for such non-equilibrium ...
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Tilting ratchet; need for time varying force?

With a tilting ratchet (a form of Brownian ratchet) it is often said (e.g. here) that the force applied is periodic with mean zero. As I understand it we get motion in the case of a constant force. I ...
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19 views

How can distributed point forces and torques be optimally balanced to achieve desired accelerations?

A planar rigid body (e.g. a circular disc) has N 'thrusters' scattered randomly within its area. Each thruster can be instantly aimed to any direction in the plane relative to the body and activated ...
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2answers
113 views

Temperature out of thermodynamic equilibrium

I’ve been trying to gain an understanding of non-equilibrium thermodynamics. I’ve been told that out of thermodynamic equilibrium, macroscopic state variables, such as temperature and pressure, are ...
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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
46 views

Two types of path intergrals in statistical physics - difference?

In non-equilibrium statistical physics as far as I can tell there are two types of path integrals to find conditional probabilities: Path integrals over the noise in the Langevin equation, $\vec u(t)$...
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1answer
153 views

Physical meaning of the power spectrum: information it gives about the frequency content of a noise

Consider a stationary random variable $F(t)$ representing the random force on a Brownian particle in a fluid. Suppose the autocorrelation function is given by $$\langle F(0)F(t)\rangle=Ce^{-\gamma|t|}$...
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1answer
51 views

relation between quench and entropy

After a quench in a system, it gets turbulent and maybe goes too far from equilibrium situation, so after that, how the entropy and quench relating to each other? _ also what will happen to the ...
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Doubt about first law of thermodynamics applied to a non-stationary system

First law of thermodynamics applied to a non-stationary system can be given as: Q+W = del(KE)+del(PE)+del(U) If no work in done on the system then(W=0) Q= del(KE)+del(PE)+del(U) i.e. heat ...
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1answer
232 views

Brownian motion and equilibrium

I would like to know if when you consider a system in which you have Brownian motion if it is considered a system in equilibrium or far from equilibrium and why. i.e., is Brownian motion considered as ...
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82 views

Drift kinetic equation orderings

I'm trying to derive the first order drift kinetic equation given in the book Collisional Transport in Magnetized Plasmas by P. Helander and D. T. Sigmar, section 6.5. I understand that the ...
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103 views

The role of time-reversal in detailed balance

For a stationary stochastic process (representing the internal time-evolution of a certain physical system which on average is stationary) we speak of detailed balance when, roughly speaking, the ...
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1answer
30 views

Does an activated complex have a specific heat capacity?

An example of an activated complex is two atoms so close (due to collision or attraction) that they are both in the highest energy state before reaching the lowest energy state at which they can be ...
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1answer
117 views

Are there ensembles for non-equilibrium cases?

Are there thermodynamic ensembles for off-equilibrium systems? The entropy is defined, so we should be able to extract some statistics on the system.
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Reference request for semiclassical approximations for Schwinger-Keldysh path integrals

Can some one provide some resources for understanding semi-classical approximations for Schwinger-Keldysh path integrals. Is there any discussion about instanton (and multi-instanton) (for even single ...