Questions tagged [non-equilibrium]
The non-equilibrium tag has no usage guidance.
292
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Mechanics vs thermodynamics? [closed]
Many systems of classical interacting particles resonate predominantly at a single well-defined scale although they actually should theoretically allow for broad range of behaviours.
For example, a ...
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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 ...
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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 ...
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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 ...
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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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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 $G^R(\omega)$...
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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 ...
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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 ...
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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 ...
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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 ...
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Exact form of two-time correlators in out of equilibrium evolution from factorized distributions
Suppose that the have an initial product state at some time $t=0$ written in a computational basis $|0\rangle,|1\rangle$, for instance the state $|1011010\rangle$. The associated density matrix $\...
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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 ...
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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, ...
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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 $H(x) = H_{0}(x) - f_{0}x$)
$$ W(x, 0) = \...
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Why is any real process which proceeds through non-equilibrium states necessarily irreversible?
As per the title, why is any real process which proceeds through nonequilibrium states necessarily irreversible?
The question came up when reading Callen's definition of "reversible process" ...
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Heating of a metallic 'gray body' by radiation
I am interested in a realistic model for calculating the heating of a metallic body by solar radiation.
Assumption (0) is vacuum, so neither conduction nor convection.
Assumption (1) is integration ...
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What is the relation between Kubo's formula and the Green-Kubo relations?
In one hand, Kubo's formula is used in linear response quantum mechanics to obtain response functions (conductivity, magnetic susceptibility, dielectric function) and so on in terms of correlation ...
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In NEGF electron transport calculations, what is the name of the basis that diagonalises the lead self-energies?
In an NEGF calculation describing electron transport through a field effect transistor, we write down the Green function $$G(\epsilon) = \left[\epsilon I- H - \Sigma_L - \Sigma_R\right]^{-1}$$ where $...
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Single metal Seebeck effect in a ring in the presence of a magnetic field
According to the usual Seebeck effect, you can make a loop of wire with two different metals, apply a temperature difference between two opposite sites of the ring and measure a current. See picture
...
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Nonequilibrium Greens function via a DMFT-mapped Anderson model?
Let $H = \sum_{<i,j,\sigma>}t_{i,j}c^\dagger_{i,\sigma} c_{j,\sigma} + h.c. + U \sum_i n_{i,\uparrow}n_{i,\downarrow}$ be a standard Fermi-Hubbard Hamiltonian. Let us single out one site of the ...
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How to obtain Non-Equilibrium (NE) Statistical Associating Fluid Theory (SAFT) expressions starting from equilibrium SAFT expressions?
I'm interested in applying Non-equilibrium Thermodynamics for Glassy Polymer (NET-GP) [1] framework to Statistical Associating Fluid Theory (SAFT) variations (e.g PC-SAFT [2]).
In short, the main NE→...
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Physical interpretations of non-equilibrium Green's functions $G^{<}(p, \omega)$ and $G^{>}(p, \omega)$
The greater and lesser non-equilibrium Green's function is defined as
$$
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^\...
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Higher order (order > 2) derivatives of free energy - higher cumulants in statistical mechanics
The first derivatives of free energies generally give relationships between thermodynamic conjugate pairs, like
entropy $S$ & temperature $T$
pressure $P$ & volume $V$
and so on.
The second ...
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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,
$$
P(x,t) = \frac{1}{2}\big[ P(x-a, t-\tau) + P(x+...
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Corollary of Wiener process and the the appearance of $\sqrt{t}$
One of the properties of a Wiener process is given by (taken from https://en.wikipedia.org/wiki/Wiener_process),
A corollary useful for simulation is that we can write, for $t_1 < t_2$:
$$W_{t_2} =...
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Condition for spontaneity of a non-equillibrium statistical system
As the title suggests: Is there any condition, which can determine the spontaneity of a non-equilibrium statistical system?
If it is a "thermodynamic" system, we can calculate its $\Delta G$ ...
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Can first order transitions accidentally have continuous free energy derivatives
Obviously if you define a first order phase transition as having a discontinuity in the first derivative of the free energy then the answer is no, but I'm asking about if the following situation would ...
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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 ...
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Langevin equation with hydrodynamic interaction
We know Langevin equation in the presence of an external applied force is given by,
$$ m\frac{dv(t)}{dt} = -\gamma v(t) + \eta(t) + \vec{F} $$
where $\eta(t)$ is delta correlated stationary white ...
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A charged conductor NOT in electrostatic equilibrium -- still an equipotential surface?
It is well known that "the surface of any charged conductor in electrostatic equilibrium is an equipotential surface" (Serway/Jewett; emphasis mine). I haven't found a good answer online for ...
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Can Fokker-Planck operator be turned into a hermitian operator?
We know that Fokker-Planck equation can be written as(with proper boundary and initial condition)
$$
\frac{\partial p(v,t)}{\partial t} = Lp(v,t)
$$
where $L$ is known as the Fokker-Planck operator ...
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Understanding the Markovian and Gaussian approximations in Brownian motion
I am trying to understand in the original derivation of Brownain diffusion, where does the assumption of Markovian and Gaussian nature factor in.
In Albert Einstein's original work on Brownian motion ...
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What is the entropy associated with a diffusion process?
Is it possible to calculate entropy from the solution of a diffusion equation(with natural boundary conditions) by using the formula of Shanon entropy? Could anyone help me to understand the entropic ...
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Is diffusion a nonequlibrium process?
We know that the diffusion equation can be viewed as the continuum limit of a discreet unbiased random walk.
My question is the following:
Is diffusion (or an unbiased random walk) a non-equilibrium ...
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Is it possible to define concepts like free energy in the diffusion process?
How does the idea of free energy (which we derive from the canonical partition function) fit in the domain of non-equilibrium processes like diffusion?
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What does it mean for $\omega$ to not be "real" in practice?
I am reading about landau damping and the author states that $\omega$ is never real (due to collisions).
https://cds.cern.ch/record/1982428/files/377-404%20Herr.pdf
\begin{equation}
1 + \frac{\...
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Is there a steady state for two conductors at different temperatures connected to a battery?
In order to understand better nonequilibrium statistical physics I came up with the following thought experiment. I wonder what are the requirements to obtain a steady state.
Let us consider two ...
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What is the meaning of an entropy current?
Imagine some kind of thermoionic device, where electrons jump off a metal in vacuum due to a fixed temperature bath and in the presence of a bias voltage.
In a steady state regime (and quasi-...
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Onsager's hypothesis: why is true that correlations decay with increasing time?
I am studying from Chandler's book (Introduction to Modern Statistical Mechanics) the fluctuation-dissipation theorem. Before introducing it, the book states something without really demonstrating it. ...
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What are good references to understand how Cooper pairs transport charges in superconductors?
I am trying to get a deep understanding of superconductors (in the BCS treatment) and I am now focusing on a detailed description of charge flow in superconductors. I have managed to find some partial ...
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(Detailed) Fluctuation Theorems/Relations and their implied symmetry
I'm currently reading up on non-equilibrium statistical mechanics, in particular so-called fluctuation theorems or fluctuation relations.
In Section 3.1.2 of arXiv:1205.4176, the author introduces the ...
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How can an object on top of a Norton dome start to move?
The Norton dome is a dome-shaped surface in a gravity field on the top of which a symmetrical object is placed in perfect balance.
According to Newtonian determinism, the object will remain in balance ...
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Non-Equillibrium thermodynamics in rapid evaporation of liquid by laser heating in vacuum chamber
I currently have some results that I am trying to understand. These results show the peak temperature of a crucible (w/ a 10mm diameter) filled with liquid Ag (see diagram). The surface of the liquid ...
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Time-Independent Quantum Hamiltonians and Thermodynamic Equilibrium
Suppose we have a time-independent Hamiltonian operator $\hat{H}$ of some system. We know that we can express the canonical partition function of said system as $z = \text{Tr}(e^{\beta\hat{H}})$ for ...
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