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10

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, ...


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 ...


4

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.


3

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 ...


3

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 ...


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

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 ...


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

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

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 ...


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

I would say they are not entirely the same, but it depends on the context. First the definitions: the Wigner transform of an operator $\hat{A}$ is defined as $$\tilde{W}\left[\hat{A}\right]=\int dz\left[e^{\mathbf{i}pz/\hbar}\left\langle x-z/2\right|\hat{A}\left|x+z/2\right\rangle \right]$$ and this is a strange function. You see that on the left, the ...


2

I) The question formulation (v4) leaves out some important implicit assumptions$^1$ of Theorem 5.2 in Ref.1. These are, among other things, the following four items. The word topologically equivalent should be replaced by locally topologically equivalent, i.e. in some local neighborhood. The (vector-valued) functions $g(w)$ and $h(w)$ are $o(w)$ for $w\to ...


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 ...


2

This is a topic in Non-Equilibrium Thermodynamics. There is a standard concept in Thermodynamics of "Thermodynamic Force", "Thermodynamic Flux" and so on. In the Physical Chemistry context you might be familiar with "Affinity" and "Chemical Potential". These are the mechanisms used to explain chemical reaction directions, etc. So to summarise this large ...


2

Just to add another look to the answer of Paul. As you know any thermodynamic potential has its own variables. As the function of its variables it achieves a minimum in equilibrium. Entropy is one of such potentials that can be used on the equal basis with the others. The only difference is that it achieves minimum rather than maximum. It appeared ...


2

This will run indefinitely, and it is the basis of just about every water fountain produced commercially. In a given time, the pump will move a certain volume of water from IN to OUT. That lowers the height of the column at IN, and increases the headspace over that column. Both of those reduce the pressure that column of water provides at the interface ...


2

Current fluctuations are notoriously difficult to calculate and work with. There is no simple relation between the moments of the current and corresponding density. Correlations, autocorrelations, etc. spoil any chance of a simple relation in general. There is a useful method called full counting statistics (for a review see "Nonequilibrium fluctuations, ...


2

In principle, temperature is defined only at equilibrium. In some cases, however, a system may be out of equilibrium and yet some of its degrees of freedom be in quasi-equilibrium. Consider for example a metal at low temperature where the electron-phonon coupling is small, and the electron-electron and phonon-phonon couplings are large. If you heat the ...


2

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 ...


2

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 ...


2

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 ...


2

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 ...


2

I would like to point out that Lecture 1 in the lecture entitled "Field Theoretical Methods for Non-equilibrium Transport Phenomena" in the following link: http://tfp1.physik.uni-freiburg.de/eu_www/Miraflores/ contains exactly the solution to the simple example (and more!) that you want to know.


2

Perhaps let me try to address this question based on a discussion with Prof. Frank Wilczek. This post is not going to be complete or anything. The punch line question I discussed with him: is there a set of mathematical equations from physical principles to distinguish life and lifeless beings? (say, hand in a system as an input, one can check its live or ...


1

I like the book Energy Landscapes by David Wales. It deals with various classes of complex systems (clusters, glasses, proteins) in the context of chemistry. I want to add - emergence is fraught with flaky ideas; a lot of appeals to ignorance are rooted from the idea of irreducible complexity. So because we can't, say, predict the weather from $F=ma$, this ...



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