 The question now arises that since the process has an initial state and a final state of a system, is there a path associated as the system progresses from the initial state to the final state? In a simplified state space, if you feel you could call it simply y and x, any two properties. Let us say this is the initial state, say i, this is the final state say f. What happens to the system as the process progresses from the initial state i to the final state f? There are two possibilities. One possibility is as we observe the process, it is possible that the system goes through a set of quasi-static processes for states in between. It is possible that during our observation, any time we find the system in some state of equilibrium as it goes from the initial state i to the final state f. So, it is possible that as we observe and mark the intermediate states, we will get a set of states in equilibrium, each one next to the each other and hence we will be able to draw a continuous locus from the initial state i to the final state f. So, it is possible that possibility a, all intermediate states are states in equilibrium and hence a locus from initial state i to the final state f exists and hence we can define a path. Such a process is called a quasi-static process. So, this simply means that all intermediate states are states in equilibrium and they form a locus from the initial state i to a final state f. Then at any stage during the process when we observe the system, we will find the system to be on one of these intermediate states as defined by the locus. Hence a proper path is defined and in this case we call this process a quasi-static process. On the other hand, it is possible that the system takes such a route that it is not possible for us to have a locus from the initial state i to the final state f. We know that the system was at the initial state i to begin with. We know that finally at the end of the process the system happened to be in this final state f, but we do not know what happened in between. The intermediate states were not states in thermodynamic equilibrium, in which case we cannot define a path. So, other thing is a path cannot be defined because intermediate states are not in equilibrium. Such a process is known as a non-quasi-static process. Just to indicate that a process exists from initial point i to the final state f, we quite often link them by means of a dotted line and show an arrow from the initial state i to the final state f. The location of the dotted line is of no consequence. It does not show the set of intermediate states. It only indicates that i at the tail of the arrow is the initial state, f at the head of the arrow is the final state. So, here we have an illustration on state space of, so this process, let me show it by a, is a quasi-static process. If I have another process like this, all intermediate states known, b is another quasi-static process. Whereas if I have a process which is non-quasi-static, let us say c, this is the depiction of a non-quasi-static process. Similarly, another non-quasi-static process would be or could be denoted like this. Now, notice that for process a and b, as the system goes from the initial state i to the final state f, take a point here. At some stage during the process from i to f, the system would be going through this point and that would be a state of equilibrium, that point in the thermodynamic state space. And hence, we can say that the process i to f, the quasi-static process a is different from the process i to f, the quasi-static process b. Whereas the two non-quasi-static processes i to f represented by c and another i to f represented by d are simply two non-quasi-static processes. The dotted line only links the initial state and the final state. The location of the dotted lines mean nothing. For non-quasi-static processes, we know only the initial state and the final state. So, summarizing here, a and b are quasi-static processes and c and b are non-quasi-static processes.