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16 votes
5 answers
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How does radiation become black-body radiation?

Textbooks treat black body radiation as radiation in thermal equilibrium with its environment (more specifically - with a black body): Planck's formula is essentially derived from the partition ...
Roger V.'s user avatar
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5 votes
2 answers
1k views

Black body vs. Thermal radiation

I am seeking clarification of the following terms: Black body radiation Thermal radiation Thermal light source At the first glance, the first two are the same thing, and they are the radiation ...
Roger V.'s user avatar
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8 votes
2 answers
786 views

Assumptions of thermodynamic & chemical equilibrium in fluid-dynamics

I am reading about the Euler equations of fluid dynamics from Leveque's Numerical Methods for Conservation Laws. After introducing the mass, momentum and energy equations, some thermodynamic concepts ...
smilingbuddha's user avatar
23 votes
6 answers
4k views

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 ...
Metric's user avatar
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2 votes
1 answer
7k views

The choice of pivot point in non-equilibrium scenarios [duplicate]

It is true that under equilibrium condition, no matter what pivot point one choose, the resulting net torque will always be zero. I wonder if this principle apply to non-equilibrium scenarios as well, ...
Bohan  Lu's user avatar
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8 votes
1 answer
396 views

How to dress free Green functions with constant broadening?

I want to find a way to dress free Keldysh Green functions with the simplest level broadening. But there seems to be some quite unexpected result. Let's consider free Keldysh Green functions in ...
xiaohuamao's user avatar
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1 vote
1 answer
1k views

Boltzmann equation: how to estimate the relaxation time?

A widespread approximation of the full integro-differential Boltzmann equation is the so-called "relaxation time approximation", where the collisional integral is replaced by: $$ \partial_t ...
Quillo's user avatar
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10 votes
3 answers
3k views

Book recommendation for nonequilibrium thermo/stat mech

I'm doing an undergrad research project that lies at the intersection of biology and nonequilibrium thermodynamics, but I'm starting to realize almost none of my equilibrium thermo/stat mech knowledge ...
6 votes
2 answers
895 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
4 votes
1 answer
480 views

Entropy production in non-equilibrium systems: physical interpretation?

I have been learning about entropy production in non-equilibrium systems as developed by Prigogine and others, especially in the context of chemical reactions. I now understand that from the first law ...
PianoEntropy's user avatar
19 votes
5 answers
10k views

What are some of the best books on complex systems and emergence?

I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory ...
16 votes
1 answer
3k views

Maximum Principle vs. Minimum Principle in Non-equilibrium Thermodynamics

Prigogine's Min. principle states that in steady-state non-equilibrium systems the entropy generation rate is at a minimum, i.e., a system will seek a steady-state that has min entropy generation. ...
Sankaran's user avatar
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3 votes
2 answers
521 views

Non-equilibrium phase transition

I have come across the term Non-equilibrium phase transition. And unfortunately I can't find any examples of such a phenomenon. What examples of nonequilibrium phase transitions are known? Are there ...
Nikita's user avatar
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16 votes
1 answer
2k views

Relation between Langevin and Fokker-Planck for exponentially correlated noise

What is the corresponding Fokker-Planck equation for, $\frac{df(t)}{dt}=-kf(t)+\zeta(t)$ where, $\zeta(t)$ is random noise? In particular, how will the Fokker-Planck equation look if $\zeta(t)$ is ...
nitin's user avatar
  • 475
8 votes
5 answers
2k views

How is temperature defined in non-equilibrium?

I see that temperature is defined always in equilibrium. But systems which are not in equilibrium with their environment. How is temperature defined in these cases? Humans for example, have a body ...
veronika's user avatar
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6 votes
2 answers
3k views

Modern textbook on statistical field theory with an emphasis on applications to non-equilibrium phenomena?

What is a good textbook on statistical field theory, with an emphasis on applications to non-equilibrium phenomena? I am a final-year undergraduate, have already taken introductory classes in ...
3 votes
1 answer
161 views

Turbulence, Euler equations and equipartition of energy

Recently the user CBBAM asked about the inviscid limit in turbulence and the relation between Navier-Stokes equations and Euler equations when $\nu \to 0$. There I pointed out that Onsager proposed ...
AdBahamonde's user avatar
2 votes
1 answer
813 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|}$...
SRS's user avatar
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14 votes
4 answers
432 views

How quickly should a fluid come to hydrostatic equilibrium?

Let's say I'm holding a one-liter water bottle, full of water, which I then drop. Before dropping the water bottle, the equilibrium is for there to be a pressure gradient in the water canceling the ...
Mark Eichenlaub's user avatar
12 votes
4 answers
1k views

Is "equilibrium state" equivalent to "well-defined state variables"?

Follow up to Intuitively, why is a reversible process one in which the system is always at equilibrium? and How slow is a reversible adiabatic expansion of an ideal gas? Suppose you have a piston ...
Mark Eichenlaub's user avatar
7 votes
1 answer
4k views

Calculating conductivity from Green's functions

I am trying to calculate the conductivity in the linear response regime of a disordered electron gas. (or eventually of a mean field Heavy fermion system with known one particle green's functions). I ...
Garvan's user avatar
  • 71
5 votes
1 answer
2k views

What is non-thermal plasma?

I read about non-thermal plasma, but I still have some questions: The ions and neutral particles are not in thermal equilibrium with the electron, does that mean that the overall temperature is low ...
Abdelrahman Esmat's user avatar
1 vote
2 answers
1k views

Assumption of local thermodynamic equilibrium in fluid dynamics

Moving fluids are generally in a state of non-equilibrium. However, in fluid dynamics, people generally assume a state of local thermodynamic equilibrium and argue that in such a condition, ...
Shivam Sinha's user avatar
18 votes
2 answers
2k views

Applications of the Feynman-Vernon Influence Functional

I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe non-...
user avatar
11 votes
4 answers
3k views

Diffusion coefficient for asymmetric (biased) random walk

I want to obtain a Fokker-Planck like equation by taking the continuous limit of a discrete asymmetric random walk. Let the probability of taking a step to the right be $p$, and the probability of ...
SarthakC's user avatar
  • 225
9 votes
5 answers
1k views

Sufficient and necessary conditions on random walk to obtain standard diffusion equation

In the simplest random walk model that is generally considered, the probability of the finding the particle at time $t$ in $x$, $P(x,t)$ is given by, $$ P(x,t) = \frac{1}{2}\big[ P(x-a, t-\tau) + P(x+...
user35952's user avatar
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8 votes
4 answers
2k views

Non equilibrium statistical mechanics [closed]

A question kept bothering me about the Non-Equilibrium Statistical mechanics, can somebody give a simple description of how one approaches this subject? Is there a exact formalism, as we have for ...
Jaswin's user avatar
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6 votes
2 answers
3k views

Definition of equilibrium in statistical mechanics

Equilibrium statistical mechanics is (amongst other things) about deriving the equations of state of thermodynamic systems (in equilibrium) from a microscopic basis (i.e. starting with a microscopic ...
user2224350's user avatar
6 votes
1 answer
770 views

Dynamic Renormalization group in Momentum space

I am trying to reproduce the computations of Appendix B of Fractal Concepts on Surface Growth (Barabási & Stanley), about the computation of the critical exponents of KPZ equation using Dynamic ...
Victor Buendía's user avatar
5 votes
1 answer
616 views

On the Eigenstate Thermalization Hypothesis: what does "energy eigenstates are thermal" mean?

I'm trying to understand what exactly is the ETH, and miserably failing. Here's what I'm reading everywhere: isolated systems are supposed to thermalize, hence "forget about their initial ...
user2723984's user avatar
  • 4,716
5 votes
2 answers
2k views

How to prove the Bose enhancement factor $(1+f)$ and the Pauli blocking factor $(1-f)$ in Boltzmann equation?

$$1+2\rightarrow3+4+\cdots$$ For the collision integral in the Boltzmann equation for particles obeying different statistic, the factor is 1 for classical final particles , 1-f for final fermions, 1+...
346699's user avatar
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4 votes
3 answers
224 views

Are stationarity, Markovianity and Gaussianity sufficient conditions to ensure that the random force on a Brownian particle is delta correlated?

In the Langevin model, if we make the assumption that the random force $\eta(t)$ acting on the Brownian particle is a stationary, Markovian, and gaussian process, does it automatically ensure that the ...
SRS's user avatar
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4 votes
1 answer
703 views

Active Matter Systems

Active matter is composed of large numbers of active "agents", each of which consumes energy in order to move or to exert mechanical forces. Due to the energy consumption, these systems are ...
Joe's user avatar
  • 41
3 votes
0 answers
97 views

How are boundary consitions implemented correctly in time dependent hydrodynamics?

I posted this question more than one year ago and got an answer recently. This answer looks good to me, but indicates that something is wrong in my original approach to the problem. Can someone tell ...
Steven Mathey's user avatar
2 votes
1 answer
729 views

Chemical reaction A+B$\leftrightarrow$C. Equilibrium VS Non Equilibrium

Could you please confirm or say why I am wrong? Let us consider the steady state of the chemical reaction $A+B \leftrightarrow^{k_+}_{k_-} C$, with $k_+$ and $k_-$ the forward and backward rates. ...
David's user avatar
  • 347
2 votes
1 answer
408 views

Equivalent system in Centre manifold theory

I was studying the centre manifold theory. It says (see Kuznetsov (pdf) page 155, theorem 5.2) that the system on the left side of the picture is topologically equivalent to the one on the right. $ \...
edwineveningfall's user avatar
2 votes
2 answers
318 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 ...
user35305's user avatar
  • 3,207
2 votes
1 answer
373 views

From Boltzmann equation to Lattice Boltzmann

I'm following the book Lattice Gas Cellular Automata and Lattice Boltzmann models which refers to this paper to explain how to discretize the Boltzmann equation (BE) into the Lattice Boltzmann ...
Learning from masters's user avatar
1 vote
2 answers
311 views

Reconstruction of information stored in an evaporating black hole from the emission spectrum?

For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) ...
Dilaton's user avatar
  • 9,533
1 vote
0 answers
69 views

Canonical treatment of thermalization of two gases at different temperatures

I'd like to understand the thermalization process when two gases of different species and different temperatures are allowed to mix in an insulated container, interacting only through an elastic ...
Jess Riedel's user avatar
  • 3,644
1 vote
1 answer
338 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 ...
Mitradip Das's user avatar
1 vote
2 answers
135 views

Is interchanging the orders of averaging operation with integral operation allowed?

In the book of Zwanzig, Nonequilibrium statistical physics, at page 6, after explaining Langevin equation Brownian motion, to show that $<v^2> = 3/2 k_B T/m$ consistent with the Langevin ...
Our's user avatar
  • 2,283
1 vote
1 answer
1k views

Understanding collision terms in Boltzmann equation

I am reading a paper that deals with the Boltzmann equation. They add a collision which is supposed to account for collisions which happen when particles are within a radius of $d$ from each other. ...
Julius's user avatar
  • 113
0 votes
1 answer
426 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 $$\...
Chetan Waghela's user avatar
0 votes
2 answers
526 views

Dynamical interpretation of reflecting boundary conditions in the Fokker-Planck equation

Background: For a particle driven by the dynamical equation $$ \dot{x}(t) = a(x,t) + b(x)\xi(t),$$ where $\xi(t)$ is a Gaussian white noise, the probability distribution of position $x$ is governed by ...
kevinkayaks's user avatar