Questions tagged [non-equilibrium]

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Logistic Growth: Mean Field Equation

I was told a while ago that for the logistics growth process: $$x \underset{k_2}{\stackrel{k_1}{\rightleftharpoons}}x+x$$the mean field equation for the population $n$ is given by: $$\frac{d\bar n}{dt}...
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1answer
96 views

Why is it interesting to study “quantum quench” at a critical point?

In the presentation, "Quantum Quenches in Extended Systems", by S. Sotiriadis, P. Calabrese and J. Cardy, it was pointed out that quatum quench through a critical point remains an open problem. Why ...
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1answer
631 views

How to pass for Langevin equation to Fokker-Planck equation?

What is the procedure to pass from the description of a phenomenon made by the Langevin equation: $$ \frac{dv}{dt}=-\frac{v}{\tau}+\sqrt{2c}\,\eta $$ to the corresponding description with the Fokker-...
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1answer
51 views

Why is matter wave field usually assumed to be be intrinsically stable?

In the paper "Collapse and revival of the matter wave field of a Bose-Einstein condensate" by M. Greiner, O. Mandel, T. Haensch and I. Bloch, it was stated that Bose-Einstein condensate (BEC) ...
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1answer
48 views

Uniqueness of the square-root of the diffusion matrix?

In the Langevin equation with hydrodynamic interactions the stochastic force on particle $a$ is: $$ \sqrt{2k_BT} A^{ab}_{ij} \xi^{b}_j(t)$$ where $\xi$ is a unit white noise. Here $ A^{ab}_{ij} $ is ...
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75 views

Relationship between Keldysh formalism and time-dependent perturbation theory

When treating systems in weak external time-dependent electromagnetic field we can use usual time-dependent perturbation theory or the Keldysh formalism which is tailored for such non-equilibrium ...
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2answers
147 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 ...
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1answer
164 views

Fluctuation dissipation on a ring?

The integral fluctuation theorem is given by: $$\left< e^{-R}\right>=1\tag{0}$$ where: $$R\equiv \ln \left( \frac{p_0(\vec n_0) p[\vec n(\tau),\vec c(\tau)]}{p_f(\vec n) \cdot p[\tilde n(\tau),\...
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1answer
50 views

Two types of path intergrals in statistical physics - difference?

In non-equilibrium statistical physics as far as I can tell there are two types of path integrals to find conditional probabilities: Path integrals over the noise in the Langevin equation, $\vec u(t)$...
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1answer
188 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|}$...
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1answer
55 views

relation between quench and entropy

After a quench in a system, it gets turbulent and maybe goes too far from equilibrium situation, so after that, how the entropy and quench relating to each other? _ also what will happen to the ...
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91 views

Doubt about first law of thermodynamics applied to a non-stationary system

First law of thermodynamics applied to a non-stationary system can be given as: Q+W = del(KE)+del(PE)+del(U) If no work in done on the system then(W=0) Q= del(KE)+del(PE)+del(U) i.e. heat ...
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1answer
333 views

Brownian motion and equilibrium

I would like to know if when you consider a system in which you have Brownian motion if it is considered a system in equilibrium or far from equilibrium and why. i.e., is Brownian motion considered as ...
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112 views

Drift kinetic equation orderings

I'm trying to derive the first order drift kinetic equation given in the book Collisional Transport in Magnetized Plasmas by P. Helander and D. T. Sigmar, section 6.5. I understand that the ...
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158 views

The role of time-reversal in detailed balance

For a stationary stochastic process (representing the internal time-evolution of a certain physical system which on average is stationary) we speak of detailed balance when, roughly speaking, the ...
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1answer
33 views

Does an activated complex have a specific heat capacity?

An example of an activated complex is two atoms so close (due to collision or attraction) that they are both in the highest energy state before reaching the lowest energy state at which they can be ...
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2answers
155 views

Book on statistical mechanics (including kinetics) with Maximum Entropy approach

I am looking for a book on statistical mechanics including non-equilibrium and kinetic topics. Specifically following the Maximum Entropy approach of information theory (a la Jaynes). So far I have ...
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1answer
130 views

Are there ensembles for non-equilibrium cases?

Are there thermodynamic ensembles for off-equilibrium systems? The entropy is defined, so we should be able to extract some statistics on the system.
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106 views

Reference request for semiclassical approximations for Schwinger-Keldysh path integrals

Can some one provide some resources for understanding semi-classical approximations for Schwinger-Keldysh path integrals. Is there any discussion about instanton (and multi-instanton) (for even single ...
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2answers
163 views

What rigid body rotation causes rotational viscosity?

According to the book Non-Equilibrium Thermodynamics by S. R. De Groot and P. Mazur page 309, there are some rigid body rotations causing rotational viscosity. What kind of fluid is that? How can this ...
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36 views

Is there an equivalency between fluctuation and effective degrees of freedom?

Is it possible to use the fluctuation-dissipation theorem to introduce a new "fictitious" degree of freedom (d.o.f) for an existing coordinate/d.o.f which fluctuates a lot? Consider a non ...
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1answer
404 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 ...
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1answer
98 views

Thermal conductivity of a liquid (I)

Problem statement: Thermal conductivity of a liquid increase with the density according to the expression: $$ \lambda = \dfrac{\lambda_0}{1-b(\rho-\rho_0)}$$ where $\lambda_0, b, \rho_0 >0$. ...
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2answers
169 views

Can a closed system be a non-equilibrium system?

Can a system without any interaction with other system be a non-equilibrium system; or is it that gain and loss is always needed for non-equilibrium?
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2answers
572 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, ...
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40 views

Is there a generic procedure to find Free energy functional (a.k.a. Large deviation functional) in Non-equilibrium statistical mechanics?

In equilibrium statistical mechanics, one often writes free energy functional for a system. But is there a generic procedure to find free energy functional for systems in non-equilibrium statistical ...
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168 views

Expectation values in Doi-Peliti formalism

I'm trying to understand how the Doi-Peliti (DP) action is constructed, and specifically how they compute expectation values. To this end, I've been using the book by Taüber as a reference (Critical ...
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1answer
155 views

Can you prove the interesting relation in equilibrium thermodynamics?

Problem and background I noted the following interesting relation in a paper discussing the liquid-vapor phase change, in which it was given directly without any derivation and reference: $$d\ln p^\...
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1answer
303 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 ...
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5answers
882 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 ...
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33 views

Many-particle systems where current and applied force are in opposite direction

Are there instances known (both observed or theoretic) of large-$N$ systems where applying an external force causes a current of the "corresponding charge" (present in the system) in the direction ...
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0answers
140 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 ...
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1answer
540 views

Keldysh formalism and Kubo formula

I am working on out-of-equilibrium problems of strongly correlated materials, so I am interested in the Keldysh formalism. I just started reading about the subject, and I don't understand quite well ...
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1answer
821 views

What's the meaning for the derivatives for temperature and pressure?

If we view the temperature and pressure as the function of time and space, $$T = T(x,y,z,t) \quad ; \quad P = P(x,y,z,t)$$ then what's the meaning for the following derivatives? $$\nabla T \...
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1answer
83 views

How large is the “elementary volume” in a fluid

A fluid is described as a continuum with quantities such as pressure $P$, temperature $T$, particle density $n$, and macroscopic velocity $\vec{v}$ as functions of spatial coordinates $x^i$ and time $...
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2answers
1k 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 ...
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1answer
63 views

Why is Bernoullis Isentropic

I have trouble understanding why we classify an inviscid adiabatic incompressible flow along a streamline as isentropic Thermodynamic definition $$dS = dQ/T$$ Adiabatic Invsicid $$dQ =0= dS$$ So ...
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3answers
144 views

Rapidly oscillating piston — work or heat?

Question An ideal gas has its volume controlled by the $x$-coordinate of a piston. At $t=0$, the piston starts oscillating very quickly (compared to the time scale of equilibration in the gas), then ...
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295 views

Master Equation -> Fokker-Planck Equation

Suppose we have the master equation $$\partial_{t}P_{n}(t)=a(n+1)nP_{n+1}(t)+b(n-1)P_{n-1}(t)-[an(n-1)+bn]P_{n}(t)$$ where $a$ and $b$ are constants. I would like to take the continuum limit of this ...
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1answer
118 views

What goes wrong for the fundamental assumption of statistical mechanics when the system is not at equilibrium?

The fundamental assumption of statistical mechanics is that, "In an isolated system in thermal equilibrium, all accessible microstates are equally probable (according to Schroeder)." So what goes ...
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2answers
85 views

How do we understand the dynamics and nonequilibrium?

In our physics classes,we have learned lots of laws to describe the motion of particles,such as Newton's second Law $$F = m \ddot x$$ in classical mechanics,and also the famous Schrödinger ...
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0answers
131 views

Does the Lindblad equation satisfy a fluctuation dissipation relation?

The fluctuation dissipation relation is usually stated in terms of an identity that relates the retarded, advanced and either the Keldysh or time-ordered correlators. This is easily enforced in ...
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1answer
752 views

Discrete Langevin Equation

We have the Langevin equation, that describes the motion of a particle in a viscous medium, given by \begin{equation}\label{Langevin} \frac{dv}{dt} = -\gamma v + \zeta(t) \end{equation} With the ...
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1answer
478 views

Size of a Brownian particle

Usually in Brownian dynamics, we consider the Brownian particle size to be much-much larger than the size of the particles of the fluid on which the Brownian particle is immersed in. In this scenario ...
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41 views

Hydrogen bonding and dichotomous Markov process

The hydrogen bonding function between water and monomer (from a micelle/bilayer) can be defined as $h(t) = 1$ if the hydrogen bond exists between the two and $h(t) = 0$, if there is no hydrogen ...
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0answers
79 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 ...
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0answers
72 views

How is zonal flow defined and computed?

The transition to turbulence in pipe flow was recently observed to be in the same universality class as directed percolation. This was done by reinterpreting the turbulence and laminar flow in terms ...
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2answers
936 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 ...
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47 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
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217 views

Violations of Onsager reciprocity?

As far as I understand it, the modern statement of Onsager reciprocity is that the linear-response transport coefficient matrix, when transposed, is equal to that of the time-reversed system (reversed ...