I am very interested in Thermodynamics, but though it is easy to find good books and information about classical thermo, it seems that is not the same for non-equilibrium thermodynamics. I would like to know what important discoveries (theoretical or practical) has the non-equilibrium thermo has made, and what things of this discipline are really worth knowing.
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2$\begingroup$ Onsager relations are maybe the most important of the old stuff. Newer developments include Mori-Zwanzig formalism (not really new), (Crooks) fluctuation theorem (FT) (also fluctuation-dissipation theorem), Jarzynski equality (JE). For example JE is actively used to compute free energies of some transitions in systems (along with the more traditional umbrella sampling and thermodynamic integration etc). I know that FT has been used to design new experiments to measure forces at the nanoscale. Langevin equation is sometimes counted as nonequilibrium thermodynamics and is really worth knowing. $\endgroup$– alargeCommented Aug 29, 2014 at 11:54
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$\begingroup$ The field of kinetic theory deals with stastically large numbers of particles whose energies are typically not distributed according to the equilibrium Maxwell-Boltzmann distribution. Kinetic theory is the foundation of plasma physics, so it has many applications. $\endgroup$– Robin EkmanCommented Aug 29, 2014 at 12:39
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$\begingroup$ Non-eq. QFT is a new and dynamic field of study that contributes considerably to our understand of how thermalization works and how things like inflation may work in toy models. A good introduction is here. $\endgroup$– ACuriousMind ♦Commented Oct 5, 2014 at 16:52
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2 Answers
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Non-equilibrium thermodynamics is an emerging field of study. Asking whether the new concepts introduced by that emerging field will prove to be of practical value is a bit premature. The concepts are only now just starting to make their way out of academia.
The concept certainly has merit. On a grand scale, a thermodynamic system that truly is in equilibrium with the external environment necessarily has a temperature of 2.72548 K (the temperature of the cosmic microwave background). All thermodynamic systems of interest to humankind are far removed from thermodynamic equilibrium.
On the other hand, does non-equilibrium thermodynamics offer anything above the simple expedient of making intrinsic quantities such as temperature, pressure, density, etc. local functions that vary within some object as opposed to global attributes of that object? Nobody teaches those simple expedients as "non-equilibrium thermodynamics"; they're part and parcel of standard thermodynamics. But if you think about it, that one has to resort to these expedients inherently means the system is not in thermodynamic equilibrium.
answered Aug 29, 2014 at 9:27
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I agree with the last part of David Hammen's answer that the discrimination between classical thermodynamics and non-equilibrium thermodynamics is sometimes a bit arbitrary and essentially a cultural trend. There is in fact nothing conceptually new in the quantities introduced: temperatures are still temperatures and so are pressures, densities and so on and the fundamental principles to be fulfilled are still the first and second principles of standard thermodynamics.
Now, I am being a bit unfair here as non-equilibrium thermodynamics worries about something that classical thermodynamics did not worry explicitly about that is the "dynamics" of thermodynamical systems.
Standard thermodynamics provides rules for picking transformations that may occur among all the possible transformations one might think of. However, it is quite silent on the subject of how long does it take to reach such and such states.
Empirical laws, which are the dynamical equivalents of the equilibrium equation of state, may be inferred from experiments (like Fick's laws and Fourier's Laws) but finding a theoretical rationale for these laws and their range of validity is one of the goals of most non-equilibrium schools of thermodynamics.
Now, if I have to name tools and theories that have been used to address this dynamical problem, I would mention (this is not an exhaustive list) Swanzig's projection method, large deviation theory, generalized fluctuation-dissipation theorems, stochastic processes and simply the linear response theory which is assumed anyway in many cases.
