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Why Does Every Member of the Ensemble Perform Work Equal to the Change in Free Energy During a Quasiequilibrium Process?

I'm studying Jarzynski's 1997 paper on the Jarzynski Equality. In the second part of the proof (from equation (9) to equation (10) in the paper), Jarzynski considers the following process: considering ...
Luessiaw's user avatar
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1 answer
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Helmholtz decomposition of flow at non-equilibrium steady state

I'm trying to work through Karl Friston's mathematical derivation of the Free Energy Principle from Langevin Dynamics (see this paper). I'm confused about the part at the end of page 8 where he uses ...
Ariel's user avatar
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What are good introductory books for contact geometry in non-equilibrium thermo?

As far as I can understand, Mrugala's paper on the geometry of thermodynamic processes covers introductory prerequisites for the contact formalism applied to thermodynamics, however, I know there's a ...
1 vote
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Meixner and the Impossibility of Non-equilibirum Entropy [closed]

Meixner in a series of publications, see a short list below, starting from 1959 criticized and ultimately denied the possibility of defining the entropy concept in an irreversible process. His ...
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Microscopic derivation of Newtons law of viscosity?

Newtons viscosity law says that viscous stress is proportional to spatial velocity gradient. When used in hydrodynamic problems it results in the Laplacian of the velocity field appearing in the ...
YoussefMabrouk's user avatar
7 votes
1 answer
93 views

Relation between time-ordered propagator in condensed matter and Feynman propagator

In particle physics I am used to the Feynman propagator being decomposed into positive and negative frequency Wightman functions. For example, this is the representation used in Eq. (6.2.13) of ...
ds283's user avatar
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0 answers
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Does Equipartition hold in overdamped dynamics?

We start with the Langevin equation $$m\frac{\mathrm{d}^{2}x}{\mathrm{d}t^{2}} = -\Gamma \frac{\mathrm{d}x}{\mathrm{d}t} +\sqrt{2\Gamma k_{B}T} \eta(t). $$ Now, we know that at $t \gg m/\Gamma$, the ...
Mayank's user avatar
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Pressure difference between a box and the outside atmosphere

Say I have a box of volume $V$, with an ideal gas inside it with temperature $T_b$. I don't know the number of particles inside it. The box is surrounded by the room's environment, which has ...
Doron Behar's user avatar
1 vote
0 answers
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Evaluating the PDF of an active Ornstein-Uhlenbeck process

I am going through this paper: Inertial Self-Propelled Particles. For a free-particle, when there is no external potential, the authors have written the stochastic differential equations as - $$\dot{\...
QuestionTheAnswer's user avatar
3 votes
1 answer
76 views

Relation between Dyson equation, Kadanoff-Baym equations and 2PI formalism

I am learning the framework of non-equilibrium field theory. Probably this is clear enough to an expert, but the expansive number of formalism, methods, and frameworks is confusing for a beginner. I ...
ds283's user avatar
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Floquet Theory and Quantum Quench

Floquet Theory and Quantum Quench are approaches to study systems far from equilibrium (e.g. periodic driving of a closed system). Floquet Theory helps to find a unitary operator $Q(t)$ such that it ...
ZHENGYAO HUANG's user avatar
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Linewidth from correlation functions

I work on cavity modes interacting with matter inside the cavity and I want to determine the linewidth of the light. I do not have excess to the state of the system directly but in a steady state, I ...
M_kaj's user avatar
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0 answers
28 views

Integration by parts to switch sign on anti-Hermitian Louivillian

I am self studying non-equilibrium stat mech and a common theme is that I am unable to reproduce the "this follow from integration by parts" parts of derivations. Here is the most recent: In ...
spleen's user avatar
  • 21
0 votes
1 answer
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Callen's Statistical and Thermo approach

In the Callen's paper pointed out two approaches for evolution of systems out of equilibrium. In one part he says The statistical approach consists of generalizing the methods of statistical ...
Testina's user avatar
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2 answers
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Understanding how entropy works [closed]

I need to have a fully functioning understanding of entropy so I've got a few questions to ask What are the conditions for an increase in entropy to be reversible? I (think) I know that any process ...
manoroli's user avatar
-8 votes
3 answers
217 views

How Taylor series is compatible with special relativity?

In mathematics, an analytic function is defined by its possession of a Taylor series with a positive radius of convergence ($R_c​>0$). Notably, certain analytic functions—such as holomorphic ...
Omid's user avatar
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4 votes
0 answers
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How much entanglement does each quasiparticle carry?

The dynamics of entanglement entropy $S$ out of equilibrium can be understood in some regimes from the point of view of the quasiparticle picture: an excited state acts as a source of pairs of ...
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The Relation btw Clausius' and Boltzmann's Statements of the 2nd Law during a State Change within a Finite Time Interval

In his book, Non-Equilibrium Thermodynamics and Statistical Mechanics, Attard takes an approach to deduce a relationship between the probability of state (Boltzmann's statement of the 2nd Law) and the ...
Kaveh Rad's user avatar
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0 answers
29 views

A general approach to choosing/deriving response functions?

I'm interested in applying some simple linear response theory to a (weakly) non-equilibrium system. For example, consider a microscopic rigid body attached to a wall at a certain point, and that this ...
oofin's user avatar
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1 vote
0 answers
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Self-energy of a spinon coupled to a $\rm U(1)$ gauge field

I would like to understand how to calculate the 1-loop self-energy for spinons coupled to a $\rm U(1)$ gauge field. For context, I am going through Nagaosa & Lee's "Gauge theory of the normal ...
dumbpotato's user avatar
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Whether there is an isolated system, it will enter equilibrium [duplicate]

For a thermodynamically isolated system, will it eventually move toward thermal equilibrium? Will there be exceptions to the system?
zhou's user avatar
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3 votes
1 answer
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Observables expressed by the lesser Green's function $\tilde{\mathcal{G}}^{<}(k, E)$

I am reading the paper PRB 106, 035102 (2022). In the supplementary materials, it says, within the Green’s function formalism, the thermal and quantum average of an observable θ is expressed as, $$\...
vcuteym's user avatar
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0 answers
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Partition function in Non-equilibrium field theory in statistical mechanics

Consider a system that described by the Hamiltonian $H(t)$, contains non-adiabatic time-dependent external fields and the evolution drives the system away from equilibrium. Now the partition function ...
Santanu Singh's user avatar
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Keldysh contour and time-dependent observables

How to use the non-equilibrium Keldysh Green's function to solve a driven harmonic oscillator? A quantum harmonic oscillator $H_0 = \omega_0 a^\dagger a $ is coupled to a pump field E(t) (refer to ...
vcuteym's user avatar
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2 votes
1 answer
57 views

Meaning of Gibbs average

This might sound a very amateur question but I couldn't find the answer anywhere. Simply, what is the meaning of Gibbs average? I've came across this term on the paper: Transmission of Information ...
duodenum's user avatar
1 vote
0 answers
75 views

What are the differences between stationary and nonstationary black holes?

I am a bit confused about what are the properties that hold for black holes in general and which ones only hold for stationary black holes. Let me try to explain what I know and hopefully people can ...
P. C. Spaniel's user avatar
1 vote
1 answer
69 views

Entropy for non-equilibrium processes

How can one derive a general expression for the entropy production in a system undergoing a non-equilibrium process, such as a non-equilibrium phase transition or a stochastic fluctuation?
Qwerty's user avatar
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How do you determine the Pull Direction for a GROMACS umbrella sampling simulation to generate the most accurate free energy value?

I am trying to calculate the free energy between a protein and aptamer using GROMACS. Literature has indicated that one of the best way to do so is by performing an umbrella sampling MD simulation ...
unit vector's user avatar
1 vote
0 answers
32 views

Detailed derivations about Mode Coupling Theory (MCT)

I am currently reading two articles related to mode coupling theory (MCT) and I am stuck in evaluating some ensemble averages, since there is no detailed derivations given. Moreover, the two ...
Jiho Son's user avatar
-1 votes
1 answer
58 views

What is an good book to study classical non-equilibrum thermodynamics? [duplicate]

I am a physics student who has just started my master's program and am taking a course on classical non-equilibrium thermodynamics. I am looking for a book that can help me learn this subject. Are ...
1 vote
0 answers
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Application of Schwinger-Keldysh formalism in various topics except cosmology

I want to find some theories or models on Schwinger-Keldysh formalism (in-in formalism) focusing on flat spacetime in terms of correlation functions. For example, I know there are many applications ...
0 votes
1 answer
26 views

Is it possible for a droplet to condense in the middle (bulk rather than boundary) of the vapor without impurity?

As a rule of thumb, vapor condensation usually happens at the interface between the system and the heat reservoir. Now, according to my analysis below, it is the only way for vapor to condense, which ...
Bababeluma's user avatar
3 votes
1 answer
115 views

A question on relaxation time approximation

I was learned that the form of collision term in relaxation time approximation is set to be: $$\left (\frac{\partial f}{\partial t}\right)_c=-\frac{f-f^0}{\tau}$$ in with $f^0$ is local equilibrium ...
Haiqin Tang's user avatar
2 votes
1 answer
108 views

A problem in solving a PDE of the time-ordered Green function

In the article written by Jauho in 2006 Introduction to the Keldysh nonequilibrium Green function technique, I've tried to operating with whether $g_{k\alpha}^t$ or $g_{k\alpha}^{-1}$ from right to ...
Meiu's user avatar
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0 answers
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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 ...
jywu's user avatar
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2 votes
0 answers
43 views

If a system lies in a non-equilibrium state initially, and there are two possible equilibrium final states. How does the system evolve? [closed]

This should be the area of non-equilibrium thermodynamics. The system is in a non-equilibrium state and after a long time it will evolve into an equilibrium state. But now we have two possible final ...
Mark_Phys's user avatar
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1 vote
0 answers
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Can the Keldysh occupation function have a zero for bosons or a pole for fermions?

In the Keldysh framework for nonequilibrium dynamics of quantum systems we learn that there are essentially two Green's functions that characterize a system: the retarded Green's function $G^R(\omega)$...
Jonathan Curtis's user avatar
1 vote
2 answers
181 views

Electrostatics of non-equilibrium situations

In footnote 1 of Chapter 13 of Ashcroft and Mermin, they remark that The only case we shall discuss in which the local equilibrium distribution is not the uniform equilibrium distribution (13.1) (...
EE18's user avatar
  • 1,095
1 vote
0 answers
28 views

Distinguishing between equilibrium and non-equilibrium distributions?

Suppose a physical system is described by some effective double-well potential landscape with fluctuation-driven motion along this landscape. If we watch the system for a sufficiently long time and ...
YoussefMabrouk's user avatar
1 vote
0 answers
69 views

Boltzmann equation for Lennard-Jones particles?

In the Vlasov variant of Boltzmann equation, the Coulomb pair forces are included via the force term that appears as the prefactor of the derivative of the density with respect to velocity. In that ...
YoussefMabrouk's user avatar
3 votes
1 answer
213 views

Deriving diffusion coefficients from Newtonian mechanics of Lennard-Jones phases?

The diffusion coefficient is known in the traditional physical literature as an empirical parameter of Fick's law. Here the observation is that spatial gradients of densities are suppressed by a rate ...
YoussefMabrouk's user avatar
0 votes
0 answers
73 views

From Newtonian mechanics to Boltzmann (or statistical) mechanics

Classical mechanical systems observable on a dynamical scale are subject to Newton's laws. In this case, knowledge of the Hamiltonian allows us to minimize energy taking into account inertia. This ...
YoussefMabrouk's user avatar
1 vote
0 answers
80 views

Nonequilibrium green function for interacting systems

In this book by Ryndyk on quantum transport, p. 89, the retarded single-particle nonequilibrium Green function for a non-interacting nanosystem coupled to semi-infinite reservoirs of non-interacting ...
Rudolf Smorka's user avatar
3 votes
1 answer
333 views

Issue deriving Fokker-Planck equation starting from Boltzmann's equation

I was trying to derive the Fokker-Planck equation starting from the Boltzmann's equation and I run into some issue while trying to do so. Starting from Boltzmann and using the notation $f \equiv f(x, ...
Syrocco's user avatar
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0 answers
94 views

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
0 votes
2 answers
161 views

Why is any real process which proceeds through non-equilibrium states necessarily irreversible?

As per the title, why is any real process which proceeds through nonequilibrium states necessarily irreversible? The question came up when reading Callen's definition of "reversible process" ...
EE18's user avatar
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0 votes
1 answer
56 views

Heating of a metallic 'gray body' by radiation

I am interested in a realistic model for calculating the heating of a metallic body by solar radiation. Assumption (0) is vacuum, so neither conduction nor convection. Assumption (1) is integration ...
TomS's user avatar
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2 votes
0 answers
218 views

What is the relation between Kubo's formula and the Green-Kubo relations?

In one hand, Kubo's formula is used in linear response quantum mechanics to obtain response functions (conductivity, magnetic susceptibility, dielectric function) and so on in terms of correlation ...
Mauricio's user avatar
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1 vote
0 answers
110 views

Single metal Seebeck effect in a ring in the presence of a magnetic field

According to the usual Seebeck effect, you can make a loop of wire with two different metals, apply a temperature difference between two opposite sites of the ring and measure a current. See picture ...
Mauricio's user avatar
  • 5,568
5 votes
2 answers
247 views

Physical interpretations of non-equilibrium Green's functions $G^{<}(p, \omega)$ and $G^{>}(p, \omega)$

The greater and lesser non-equilibrium Green's function is defined as $$ G^<(r, t) =\pm \frac{1}{i}\langle\psi^\dagger(0, 0)\psi(r, t)\rangle,\qquad G^>(r, t) =\frac{1}{i}\langle\psi(r, t)\psi^\...
Hao's user avatar
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