# Questions tagged [non-equilibrium]

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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 ...
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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 ...
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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 ...
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### 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 ...
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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 ...
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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 ...
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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 ...
36 views

### 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 ...
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### 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 ...
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1 vote
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### 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 ...
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1 vote
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### 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?
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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 ...
1 vote
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### 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 ...
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### 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
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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 ...
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### 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 ...
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### 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 ...
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 ...
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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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### 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 ...
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1 vote
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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 $G^R(\omega)$...
1 vote
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) (...
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### 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 ...
1 vote
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 ...
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 ...
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 ...
1 vote