Questions tagged [non-equilibrium]

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Projection operators in non-equiibrium statistical mechanics - non-euclidean function space

In the formalism proposed by Zwanzig and Mori [1,2] for projection operators, an inner product is defined for the variables of phase space which is given by, $$ (A,B) = \int d\Gamma f_{eq}(\Gamma)A(\...
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Formalism for an open system with non-adiabatic (non periodic) time dependence

Most non-equilibrium statistical processes of open time dependent systems are approached by Markovian dynamics of a system where time dependence of the system is assumed to be adiabatic (if Floquet ...
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18 views

Simple illustration for Gibbs free energy

It is believed that for complex non-equilibrium open systems an important role is played by Gibbs free energy. There are hypotheses that minimization GE helps explain the features of the evolution of ...
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58 views

What is meant by “linear” in non-equilibrium thermodynamics?

I'm trying to learn a bit about non-equilibrium thermodynamics, and am currently reading de Groot and Mazur. In it, there is a quote right in the beginning, talking about the phenomenological ...
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52 views

Reference request: Langevin dynamics of particle in high dimensional quenched random potential

I would like to have some reference (either papers or books) for the study of the Langevin dynamics (out of equilibrium, non asymptotically) of a particle $X(t)\in \mathbb{R}^N$ in a quenched random ...
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231 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 motors which may consume energy from the environment to move and exert force on ...
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26 views

Where can I find careful discussions of equilibrium?

I want to know what physical equilibrium is precisely. I'd like to understand dynamical equilibrium vs. static equilibrium, and I'd like to understand approaches to understand non-equilibrium ...
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2answers
118 views

Probability density during equilibration

An ensemble of states $x$ are initially drawn from a non-equilibrium probability density $P_0(x)$. Over time they will evolve towards the equilibrium distribution $P_\mathrm{eq}(x)$. What I want to ...
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29 views

Is there a classical correspondence of the entanglement entropy in isolated quantum systems?

For an isolated quantum system, one can study the time evolution of entanglement entropy after a quantum quench (always a pure state), which has a rich behaviour in various different models. However, ...
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1answer
61 views

How did Carnevale et al. could argue mass in a ballistically aggregating systetm evolves as $t^{2d/(d+2)}$?

I am trying to understand this paper but I am not able to do it. Please help. See the paper here. First of all how could they write collision time $t_0$ as given there?. I am not able to get it even ...
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50 views

What is the BKT transition in non-equilibrium systems?

There is a useful page on the BKT (or KT) transition here which describes the role of vortices in 2d equilibrium systems. I am interested in what happens in 2d non-equilibrium driven-dissipative ...
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29 views

Example of two-dimensional Langevin equation?

I am looking for an example of a langevin-equation with two variables: $\dot{x}=f(x,t)+\omega, x=(x_1,x_2)$. Can anyone suggest one?
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Is thermodynamics only applicable to systems in equilibrium?

So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind ...
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43 views

Accurate derivation of electron-phonon scattering contribution to metal resistivity

My lecture derived the expression for this contribtuin using the collision integral approach but I missed lot of details. He considers the lowest order correction to distribution function $f=f_0+\...
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81 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)...
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33 views

Derivation of Feynman rules from generating functional for non-eq QFT

I consider Yukawa non-equilibrium theory with interaction $g\bar{\psi}\phi\psi$ with massive fermionic field $\psi$ with mass $m$ and massive scalar field $\phi$ with mass $M$. I would like to ...
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39 views

Non-eq QFT: functional formalism

I am looking for references (papers, books etc.) where I can find pedagogical introduction to non-eq QFT without hamiltonian approach. I mean that an author start from writing down the generating ...
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52 views

Question about the Markovian property of the velocity of a Brownian particle following Langevin equation

I'am now studying Langevin model and Fokker-Planck equation with the lecture notes by Borghini Topics in Nonequilibrium Physics (NB: PDF). On page 92, he talks about the Markovian property of the ...
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48 views

Landau Theory of fluctuations

With respect to chapter 12 in the book Statistical Physics(Part 1) by Landau and Lifshitz, I am currently stuck at the intepretation of Fluctuation theory that Landau provides. In the neighbourhood of ...
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1answer
36 views

How is heat dissipation rate the product of force and velocity?

Let $q$ be heat dissipation to midium, $F$ be the force to a particle, and $\dot{x}$ is the velocity of it. According to the equation (8) in Seifert 2005, $\dot{q} = F \dot{x}$ holds. How does this ...
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1answer
70 views

Entropy production, local thermodynamic equilibrium and adiabatic process

It is said that for local thermodynamic equilibrium the local entropy production needs to be 0. Now, I am reading the following from the book by de Groot and Mazur "Non-Equilibrium Thermodynamics". ...
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1answer
49 views

Equilibrium and non-equilibrium thermodynamic states?

I have the following two states. I have classified them as equilibrium and non-equilibrium and I am not sure if that is the right category my problem is I need to understand what parameters to look ...
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18 views

Thermalization and structure formation, starting with a pure state coupled to heat bath

I am looking for tractable quantum mechanical systems which show thermalisation and/or structure formation. One idea is a small quantum system S, e.g. a quantum Heisenberg model in a pure state (the ...
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1answer
44 views

Can spontaneous fluctuations cause instantaneous non-equilibrium?

The fluctuation-dissipation theorem says that the linear response of a given system to an external perturbation is expressed as the fluctuation properties of the system in thermal equilibrium. Does ...
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1answer
75 views

Does the First law of thermodynamics hold if the final state is NOT in equilibrium?

So we know the first low of thermodynamics holds for isolated systems $$\Delta E = W+Q\tag{1}$$ Now assuming we are in a thermally isolated system such that $(Q=0)$ we obtain $$\Delta E= W\tag{2}$$...
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162 views

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

In this paper(1) 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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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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260 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
171 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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35 views

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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52 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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28 views

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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31 views

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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1answer
260 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
60 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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94 views

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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1answer
105 views

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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89 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
51 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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1answer
139 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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1answer
56 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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47 views

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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39 views

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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38 views

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
74 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
30 views

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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82 views

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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28 views

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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54 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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1answer
77 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 ...