Mryntu

So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind

Is thermodynamics really never applicable to systems which are not in equilibrium, if so why should such a restriction exist?

And also it might sound silly but why is the theory called "thermodynamics"- specifically the "dynamics" part?

It entirely depends on what you think "thermodynamics" is.

The traditional idea of thermodynamics dealing with systems whose macrostate can be fully described by e.g. temperature, pressure and volume indeed only applies to systems in equilibrium. Of course, as an approximation it also applies to systems "not far" from equilibrium, for some suitable notion of "not far", explaining its success in describing nevertheless a plethora of phenomena that occur in the real world.

However, non-equilibrium thermodynamics also exists, and is well and alive as a subfield of both classical and quantum physics. Its methods, however, differ strongly from what is commonly referred to as "thermodynamics" in introductory textbooks.

Strictly speaking thermodynamics only describes systems at equilibrium or systems which undergo some change, at the end of which they have time to relax back to an equilibrium state. The signature of a thermodynamic system is the huge reduction of the number of degrees of freedom required to describe the state of the system.

Non equilibrium is a weak characterization and actually one can distinguish different levels of departure from thermodynamic equilibrium.

For example, hydrodynamics corresponds to a case where, due to a macroscopic movement of the fluid, if the flow is not too complex, a three dimensional velocity vector field is required, in addition to a couple of thermodynamic scalar fields which describe the local thermodynamic equilibrium.

The special case of thermodynamic systems brought slightly out of equilibrium is also interesting. In that case it is possible to study the fluxes which try to restore equilibrium and to get information about transport coefficients.

However, one has to take into account that major departures from equilibrium are possible, basically requiring to go to detailed descriptions using a huge number of degrees of freedom.

When dealing with thermodynamics, you are interested in knowing the values of thermodynamic variables such as temperature, pressure, volume, entropy, etc of the system, and we assume that these quantities have uniform values throughout the system. For non-equilibrium systems, this assumption may not hold. For example, if you heat a liquid in a container, different fluid parcels may have different temperatures.

To answer your question about the nomenclature, thermodynamics evolved when people started studying heat engines and how "heat moved" from one body to another. So heat(thermo) and movement(dynamics).