# Tag Info

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Different people have different definitions of dynamical phase transition. At present, a widely accepted one is by Heyl et al. See their original paper Dynamical Quantum Phase Transitions in the Transverse Field Ising Model. Basically, it means some quantity (e.g., the fidelity) as a function of time is non-analytical at some critical times. See the cusps ...

11

The book Quantum dissipative systems by Weiss dedicates a subsection to the Feynman Vernon method, see also the original reference. See also this article and chapter 18.8 of the book by Kleinert. It's applied to the Caldeira-Leggett model, which is a toy model for a particle in contact with a heat bath. There are a number of mesoscopic systems out there in ...

8

One of the avenues to search for an answer is the so-called Keldysh formalism which is used extensively in condensed matter, in particular in mescopic physics, to define and study steady-state and time-dependent quantum phenomena in systems with infinitely many degrees of freedom. A recent comprehensive review is given by Kamenev and Levchenko, arXiv:0901....

8

Of course the name implies that time is involved somehow. People talk about dynamical thermal and quantum phase transitions and in one case you will rapidly change temperature, while in the other state defining parameter (say pressure or field etc.). We will consider thermal PT. Now what does it mean rapidly? Let us consider 2-d order phase transition as ...

6

I think that the key requirement is that the material be in local thermodynamic equilibrium. Even if it is a dynamic situation with mass flow or shock waves running through the material under consideration, if the material is in local thermodynamic equilibrium at every instant in time, then equilibrium thermodynamic concepts such as temperature, pressure, ...

5

In principle, nonequilibrium statistical mechnaics is exact like quantum theory in general. But to do actual computations in realistic systems you need to resort to approximations. For modern expositions, I'd recommend the books ''The theory of open quantum systems'' by Breuer and Petruccione and ''Beyond equilibrium thermodynamics'' by Öttinger.

5

Strictly speaking there are no reversible processes in Nature; it is an idealization that enables one to get bounds on efficiency of nonequilibrium processes by using techniques of equilibrium thermodynamics only. A reversible process is therefore primarily a theoretical concept for discussing what would happen in a process if dissipation were absent. It ...

5

Part of my PhD thesis was on this stuff, so I hope I can give a satisfactory answer. Maximum entropy production and minimum entropy production are different types of principle with different domains of application. Before discussing the answer I should make clear that the maximum entropy production principle (which I'll call MaxEP) is really a collection of ...

4

Chapter 16 of Classical and Quantum Mechanics via Lie algebras contains a section on deriving stirred chemical reaction dynamics on a statistical basis. (It is silent about the space distributed case.) Section 14G of the first edition of the Statistical Physics book by L.E. Reichl treats chemical reaction dynamics distributed in space. (The section seems ...

4

Non-thermal is a broad catch-all for energy distributions that are not Maxwellian. The reason it is interesting is because if it's not Maxwellian, it's not in thermodynamic equilibrium and some work can be extracted from it while it relaxes or the energy differences between electrons and ions produced an interesting or desirable phenomena. So to answer your ...

4

There exist an exact formalism to treat non equilibrium statistical mechanics. You start to write down the Hamiltonian for the N interacting particles. Then you introduce the distribution function in the phase space $f(r_1,r_2...r_n,p_1,p_2,...p_n,t)$.The time evolution of this distribution function is generated by the Hamiltonian and more precisely by the ...

4

I can try to sketch out the general idea here, but my deduction may not be very precise (please refer to your books to check out the coefficients and sign conventions). So I guess the question is that given a free Fermion system described by the following action $$S=-\sum_k\psi_k^\dagger G^{-1}(k)\psi_k, ...(1)$$ where $G(k)=-\langle\psi_k\psi_k^\dagger\... 4 Just to give an account of some of the most popular approaches that I have met so far about out of equilibrium thermodynamics and corresponding generalized definitions of entropy and thermodynamic potentials. On one end of the spectrum, on can follow a statistical inference approach to statistical mechanics in its very foundation (as it has been proposed ... 4 Although not a complete answer, one place to start is with the coldest naturally occurring place in the universe, which is the Boomerang Nebula, a planetary nebula that is around 1 K. As best as I can tell, this cooled below the CMB temperature simply by adiabatic expansion, and is insulated in its interior from CMB heating. Is this a feasible way to get to ... 4 You seem to only have a blurry idea of the hydrodynamic approach, so I will add a tad more about the whole idea, mainly to give you a better intuition. Hopefully this will be a useful addition to Samuel Weir's wonderful answer. A hydrodynamic state is described by the variables: mass density field, energy density field and momentum density field. These are ... 3 The roll off deviation appears to mostly be due to difficulties with accurate measurements at low magnitudes. In order to preserve the GR law you'd need to exhaustively record all earthquake measurements below the roll off magnitude and this is largely infeasible. A good example to look at (figure 3.1) is the difference between the Sumatra 2004 and Kobe ... 3 The macroscopic theory of non-equilibrium physics is called fluid dynamics. This theory is analogous to thermodynamics for the equilibrium case -- there are no assumptions about microscopic degrees of freedom. The theory that replaces classical statistical mechanics is classical kinetic theory, originally developed by Maxwell and Boltzmann. The theory ... 3 Maybe these three lectures about emergence could be interesting to get a first overview of the topic. Therein Prof. De Deo explains for example that emergence has a lot to to with what new phenomena can occurre when coarse graining (or renormalizing) microscopic degrees of freedom of a large system to obtain an effective (possibly including emergent ... 3 For clear expositions on the relationship between entropy and information, and the foundations of the non-equilibrium theory, it's well worth surfing through papers by Edwin Jaynes. You can find his full bibliography here. It's probably best to start with one of his later papers, since they take a more pedagogical approach. I would recommend 'The Evolution ... 3 Entropy is a broad topic, and very important both to physics and information theory. In general entropy is a measure of not knowing things. So a state of high entropy is when there are many possible sequences or many possible micro states of a physical system. In information theory it is $$S(\{p_i\}_i) = - \sum_i p_i \log(p_i).$$ In particular, when it is ... 3 The definition of temperature through Maxwellian and Boltzmann distributions have certain problems in quantum mechanics. In thermodynamics temperature is usually defined through the derivative of entropy as you say: $$\frac{1}{T} = \frac{\partial S(E,\mathbf{V})}{\partial E}. \qquad (1)$$ The division of the system into different parts (or different ... 3 What you are asking for is how to treat out-of-equilibrium fenomena, and as such, if it is still possible to use traditional ensemble formalism to it. I don't know about using ensembles to out-of-equilibrium thermodynamics (macro-state via micro-state counting), but I do know that you can approach these problems via kinectic theory (Boltzmann Equation and ... 3 You might want to have a look at the work of Gavin Crook (http://threeplusone.com/gec/), especially the first two chapters of his PhD thesis (to be found on his website) are quite revealing. I'll quickly summarize his main result: Assume a system is what he calls microscopically reversible, that is, the probability of a trajectory through phase space is ... 3 You can find in a separate post a rigorous prove that the evolution operator associated to your Hamiltonian is (modulo some phase terms) the displacement operator, which generates the coherent states from the vacuum. The details of the calculation can be found there http://physics.stackexchange.com/a/46389/16689 and essentially mean that, as soon as ... 3 A proper derivation of the Boltzmann equation from non-equilibrium quantum field theory (which will give the factors$1\pm f\$ in the weak coupling, quasi-particle dominated, limit) is a difficult problem. The standard reference is Kadanoff and Baym, Quantum Statistical Mechanics. The standard approach in introductory text books (and indeed, historically, ...

3

In my opinion, the reason to be of the Keldysh formalism is that it is the way to write a path integral for non-equilibrium quantum systems. It provides an action which can be used to sample paths for out-of-equilibrium systems. This is great because it opens the door to the huge toolbox of equilibrium quantum field theory to non-equilibrium problems. I can ...

3

The conclusion is correct: for any system containing a single reaction, there exists an equilibrium (with detailed balance) for any values of the rate constants. I'm not sure what's meant exactly by "equilibrium tools," but it's true to say that there's no real difference in the kinetics of an equilibrium or non-equilibrium system if it only contains one ...

2

I've started to take Jaynes' wacky point on this subject more seriously --- the key is experimental reproducibility, of which equilibration is a helpful but neither necessary nor sufficient condition. The point is that you know you have enough "macroscopic" degrees of description when you find that it is sufficient to reproduce the phenomena you are ...

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