How to conceptually identify reversible and irreversible processes? When I studied thermodynamics for the first time I didn't really get much the conceptual understanding on reversibility, but nonetheless I've got a rough understanding and a mathematical criterion for it.
The rough understanding I got was the following: If we consider a process connecting two equilibrium states we might ask whether the inverse process could occur naturally or not. If it can the process would be reversible and otherwise it would be irreversible.
The criterion for a reversible process would be $\Delta S =0$. The whole point is that the entropy maximum postulate states that the entropy must be maximized. If when a constrant is removed a system goes from $A$ to $B$ with $\Delta S > 0$, then certainly $S_B>S_A$, hence naturally the system could never return from $B$ to $A$, because it wouldn't maximize the entropy.
On the other hand if $\Delta S = 0$, we would have $S_A = S_B$ and nothing would prevent the return.
This is a mathematical criteria and more than that, requires the idea of entropy.
My question here is: suppose we are simply given the description of a process (for example: "a piece of hot metal is thrown into cold water" or "a pendulum with a frictionless support swings back and forth"), in that case we don't know the fundamental relation, and there's no mathematics whatsoever here.
In that case, just from a conceptual description of a process how can one judge whether the process is reversible or irreversible? What is a criterion that can be used when we are discussing the process just conceptually without math involved and without any knowledge about entropy?
 A: There are two techniques that I use for simple situations.
First, can I actually imagine how the reverse process would work? Intuitively, it makes sense that I can just push a pendulum back to the original state. But obviously, if I were to put a piece of room temp. metal in room temp. water, they wouldn't suddenly diverge in temperature. This is essentially just playing the system backwards in time, and seeing if it follows your intuition. Knowledge about entropy helps though.
The other technique stems from the mathematicians definition of invertible functions. If multiple initial conditions can result in the same outcome, then the situation isn't invertible. For example, slightly hotter metal and slightly colder water result in the same outcome: so there would be no way to know which original situation to pick if you tried the inverse. A caveat though: it is very hard to tell when situations are exactly identical, as opposed to nearly identical. If they are just nearly identical, then the system could just be chaotic (large dependence on initial conditions) but reversible.
However, these can become difficult to apply in complex scenarios; that's why the entropy definition is so powerful, and why we use it.
A: For a closed system, if there is no viscous dissipation of mechanical energy during the process, no finite rate of heat conduction, no finite rate of species diffusion, the process is reversible.  Under such circumstances, the process path between the initial and final equilibrium states of the system consists of a continuous sequence of thermodynamic equilibrium states.  The system is never more than slightly removed from being at thermodynamic equilibrium.
