Can equilibrium thermodynamics be used to analyze irreversible processes?

Question

As usually taught in undergraduate courses, classical thermodynamics is actually thermo-statics, the thermal physics of equilibrium states. Even in this very restricted form it can and does make important theoretical and very practical statements regarding efficiencies of energy transfer, phase equilibria, the stability of its equilibrium states, such as the maximum entropy principle for adiabatic systems and its various consequences, etc., but it leaves out how those states and their transformations are approached in time.

Since all the concepts and theorems of classical thermostatics assume equilibrium states and the reversible processes connecting them are nontemporal sequences of equilibrium states, I would like to know if and how these are useful in the study of irreversible processes? What ideas and concepts are kept and what are modified or even completely rejected as one attempts to generalize thermostatics to irreversible thermodynamics.

Answer 1

Equilibrium thermodynamics is all about equilibrium states, of course. This means the system's state is represented with a point in the phase space (PVT space for simple, hydrostatic systems). In this sense, you can study reversible processes since they are quasistatic and therefore we can draw them as a continuous line in the phase space: the system is at equilibrium every time.

We can also study irreversible processes or even non-quasistatic ones with equilibrium thermodynamics if we like, but there's a catch: since this science can only study equilibrium states, we would need for the process to begin and end in an equilibrium state, which is not so restrictive (e.g: tank of water we heat up and then stop applying heat to it until it goes back to its initial state). Therefore, you can use equilibirum thermodynamics to study global processes. You can only know the net effect of the process on your system. This is due to the fact that thermodynamic potentials are state functions and therefore they only take into account the first and the last point of the process to calculate their variation (again, under the assumption that at least these two states are equilibrium states).

Of course, you can use some tricks to approximate real world processes to quasistatic ones. For instance, you can make the system reach several states of equilibrium consecutively, which would all be drawn on the same curve in the phase space (your quasistatic, ideal process). Nonetheless, reversible processes are much harder to replicate in real life, if possible. If you are interested in finding the time dependence of your magnitudes, then you should use non-equilibrium thermodynamics. Note that, since your magnitudes depend on time, processes will no longer be quasistatic (and therefore won't be reversible either), as in a quasistatic state the system takes "infinitely long time" to go from an equilibrium state to the next one (as the name suggests)

Answer 2

Non-equilibrium states come in broadly two types. In one type the system overall is not in equilibrium but if you divide it up into many parts then each part on its own can be treated to good approximation as in equilibrium and evolving quasistatically as it interacts with surrounding parts. Ordinary thermodynamic reasoning has a lot to offer in this situation. One discovers that entropy of the total system grows, and free energy of a system in contact with a reservoir falls, etc. One gets le Chatalier's principle and one can determine directions of many chemical reactions and things like that. Concepts such as temperature, pressure and chemical potential still apply to the parts.

The second type of non-equilibrium state is where the above approximation cannot be made. This happens in turbulence and in the details of phase transitions, among other things.