Questions tagged [non-equilibrium]

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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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Finding the stress tensor in the Stokes equation from free energy

I have found free energy for a system of particles. The free energy is a functional of a scalar field which is the area of the particles. So I have the following free energy $F(A,p)= \int dx dy \: f[A(...
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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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Constructing a time homogenous approximation of a non-equilibrium time-dependant diffusion processes by time-averaging?

I am trying to formally describe and understand the consequences of an approximation that feels intuitively correct and possible to me. Is it possible to construct a time homogenous approximation of a ...
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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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Out-Of-Time-Correlators for free and interacting field theories

Consider the Out-Of-Time-Correlator (OTOC) $$ \mathrm{Tr}\left[ - [ \phi(t,\mathbf{x}) , \phi(t',\mathbf{x}') ]^2 \rho\ \right] $$ where $\rho$ is some initial density matrix, and $\phi$ is a quantum ...
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How is Newton's first law compatible with transport equations?

So, I'm studying non-equilibrium thermodynamics and the first thing I've learned is that the discipline has a first scope of generalizing the idea of transport equations. Transport equations are ...
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Intuition about non-equilibrium Green functions

In the following paper by Fotso and Freericks, the definitions of the Green functions are given as \begin{align} G^<(t,t') &= i \langle c^\dagger(t') c(t) \rangle \\ G^R(t,t') &= -i \theta(...
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Is there a fermionic fluctuation-dissipation theorem?

Question: is there any fermionic version of fermionic fluctuation–dissipation theorem? Context: In classical physics, the fluctuation–dissipation theorem is roughly written as $$\langle x(t)x(t')\...
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Doubt on obtaining Boltzmann Equation given in the book "Modern Cosmology" Ed 1, Dodelson, equation 3.9

My question refers to Equation (3.9) of Dodelson "Modern Cosmology" Edition 1, $$ n^{-3} \frac{d(n_1 a^3)}{dt}=n_1^0 n_2^0 <\sigma v>\{\frac{n_3 n_4}{n_3^0 n_4^0}-\frac{n_1 n_2}{n_1^0 ...
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Does the second law of thermodynamics hold under non-equilibrium conditions? [duplicate]

The question is just that: whether the second law of thermodynamics is always valid under non-equilinrium conditions? The origin of life involves several chemical reactions that are thermodynamically ...
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High wire artist

We want to derive a Lagrangian equations for a high wire artist which uses a balancing rod for stability purposes. We know the masses and the polar moment of inertia of the artist and the rod.
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Modifying a Boltzmann distribution to account for small deviations from equilibrium

Suppose I have a classical field whose dynamics are known. Say we are interested in a Klein-Gordon field, $$\left(\frac{\partial^2}{\partial t^2}-\nabla^2 + m^2 \right)\phi(\vec{x},t) = 0,$$ where $\...
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Rayleigh Benard Convection analyzed as heat engine?

The treatment I've seen for Benard convection in a textbook is to derive approximate equations of motion and then show that there is a periodic solution matching the boundary conditions. This is ...
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How to generate a PDE from a discrete equation in a rice-pile like model?

I am reading Noise and dynamics of self-organized critical phenomena by Albert Díaz-Guilera Here, on an extension of the rice-pile model by Bak et al demonstrating self-organized criticality. Equation ...
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2 answers
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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 ...
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Literature on non-equilibrium statistical mechanics [duplicate]

I am a graduate student, currently planning on self-studying non-equilibrium statistical mechanics. I have tried searching for literature myself, but no book/online course that I have found seems ...
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Equation of motion of a gas's center of mass due to heating

So here's a pretty basic question that I don't know how to solve within standard thermodynamics. Let's say I have a container with a gas in it. I transfer heat, $Q$, to the gas from the bottom of the ...
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Basis state of non-interacting fermions

I am trying to calculate the periodic dynamics of many-body systems (spin-$1/2$ $XY$) Hamiltonian, where, \begin{equation} H_1 = \sum_{i=1}^{N-1}(\sigma^{x}_{i}\sigma^{x}_{i+1}+\sigma^{y}_{i}\sigma^{...
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In non-equilibrium energy calculations, how do you handle negative formation enthalpies?

I'm working on some simulation software at the moment which deals with high speed flows in chemical non-equilibrium (including plasma states). When the code initially calculates total energy, it uses ...
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12 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 ...
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4 votes
3 answers
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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 ...
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3 votes
2 answers
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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 ...
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Canonical ensemble: what if the phase space density is not known?

In canonical ensemble, the probability is defined as \begin{equation} P(E)=\frac{g(E)\exp(-E/T)}{Z}, \end{equation} and the partition function is defined as \begin{equation} Z(T)=\int_0^{\infty}dE\,g(...
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4 votes
3 answers
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What happens to entropy when half the particles are removed?

Curiosity question. What happens to entropy in the following situation? A gas fills an entire container and is in equilibrium. Suddenly all particles are removed from half the container. As such, ...
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2 votes
2 answers
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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 ...
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Is entropy maximized for steadily driven systems?

Suppose we send an electric current through a piece of metal. If we knew only the average energy and current through the sample, it would seem natural to assume the state of the sample is described by ...
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Can we define the concept of temperature for a system in non-equilibrium steady state?

I would like to define the temperature for a system in a non-equilibrium steady-state. The standard textbooks show that the temperature is estimated by equating the internal energy of the system with ...
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2 votes
0 answers
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Does the fluctuation-dissipation (FD) relation $\sigma_E^2=k_BT^2C_V$ arise as a special case of the FD theorem?

The classical fluctuation-dissipation theorem states that the power spectral density $S_{\eta\eta}(\omega)$ of a classical random variable $\eta(t)$ is given by $$S_{\eta\eta}(\omega)=\frac{2k_BT}{\...
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2 votes
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What happens to the Fermi level of a metal when a dc electric field is applied?

For metals, the Fermi level $E_F$, which is also equal to the chemical potential $\mu$ at absolute zero of temperature, is the highest occupied energy level at $T=0$. In terms of the electron number ...
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How to find the determinant of a single derivative?

I am currently studying the path integral approach to stochastic processes. Recently I was reading Functional integral approach for multiplicative stochastic processes about the path integral ...
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1 answer
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Throttling process as a nonequilibrium process

From Zemansky and Dittman's Heat and Thermodynamics (6th ed.), p. 214:"A throttling process is obviously an irreversible one, since the gas passes through nonequilibrium states on its way from ...
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How to prove zero classical classical Green's function contribution

Much of the Keldysh formalism is based on the following identity $$G^{T}(t,t') + G^{\tilde{T}}(t,t') = G^{<}(t,t') + G^{>}(t,t'),$$ which using their defintions is equivalent to $$G^{\text{cl,cl}...
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Why does photocurrent need $G^<$ among other Green functions?

In this highly-cited paper (or its pdf) on photoemission, Eq.(3) gives the current density in terms of $G^<$ $$ {\bf j}({\bf r},t) = 2\hbar\left( \frac{e\hbar}{2m} (\partial_{\bf r'} - \partial_{\...
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1 answer
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Difference between kinetic and chemical equilibrium

I am currently reading up on the Boltzmann transport equation and its uses in cosmology. More specifically it is applied to particle interactions, such as 1 + 2 <-> 3 + 4. While reading through ...
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7 votes
1 answer
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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 ...
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4 votes
1 answer
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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 ...
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2 votes
1 answer
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Imaginary-time Green's Function and Nonequilibrium Green's Function

I've been learning Green's Function approach recently, following Radi Jishi's book. It says that the imaginary-time Green's function (Matsubara function) cannot be used in non-equilibrium situations, ...
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1 vote
1 answer
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Continuum Mechanics: Why would dashpot kinematics require 5 equations to specify deformation for a 2D axisymmetric problem?

I work with PEG hydrogels and use the material to recapitulate cartilage biology and I am really interested in modeling the soft tissue mechanics in COMSOL. I have been studying the work of Caccavo et ...
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2 answers
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Can we measure $\Delta G$ when a reaction hasn't reach equilibrium?

Suppose we have the reaction $$\mathrm{A + B \leftrightharpoons C}$$ The system starts with reactants (or products) and reaches equilibrium. Can we measure the change in Gibbs energy $ΔG$ at a ...
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3 votes
2 answers
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Conceptual problem about non-equilibrium steady state

I have a problem understanding what exactly is non-equilibrium steady state. Let's say the system starts with an equilibrium state at remote past. We should have the density operator given by: $$ \hat{...
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1 answer
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Does systems (such as the cell) far from equilibrium have to dissipate their energy? Can't they store it? Is there a physical requirement for that?

It is a well known fact in the field of non-equilibrium statistical physics that in order to maintain a system far from equilbrium, you need to drive it via an external energy source. The system uses ...
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Equal time Keldysh Green's function and expectation value of the F operator in the continuum notation

I recently went through Field Theory of Non-Equilibrium Systems by Alex Kamenev (2011) and I wanted to understand certain points in detail. My current problem is to understand how one can calculate ...
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5 votes
4 answers
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Is there really an inconsistency with the original Langevin equation (as claimed in the book Nonequilibrium Statistical Mechanics - V. Balakrishnan)?

I am reading the book Nonequilibrium Statistical Mechanics by V. Balakrishnan. In chapter $17$ (page $244$) he argues that the original Langevin equation has inconsistencies and should, therefore, be ...
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2 votes
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Detailed balance: What does one rigourously mean by the transition rate $dw$?

Consider (for example) non-relativistic electron-impact ionisation, in which an effectively stationary atom in state $I$ is struck by an electron of momentum ${p_1}$, producing an atom in state $J$ ...
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6 votes
2 answers
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Is entropy maximum in equilibrium?

Usually, in the context of non-equilibrium thermodynamics, it is said that entropy achieves a maximum in equilibrium, so the Taylor series expansion of entropy around the equilibrium state as a ...
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