Confusions in the 'Adhesion Theory of friction.' While reading about the Adhesion theory of friction on this site, I came to some points which I couldn't understand. I have highlighted them:

...Adhesion approach is based on the partial irreversibility of the bonding force between the atoms ... Friction is connected to adhesive irreversibility,which is how differently the surfaces behave when they stick as compared to how they become unstuck. ... Frictional force is proportional to the degree of irreversibility of the force that squeezes the two surfaces together.

What do these partial irreversibility of the bonding force and adhesive irreversibility mean? What is this irreversibility all about and what is its role in friction?
Another statement that bothered me:

Adhesive bonding at the so-called true contact points was so intense that the small fragments of the surface were continually being worn away .

What did the author mean by this statement?
Please help clearing the confusions.     
 A: The theory of friction that is described in the source is the Prandtl-Tomlinson model. I'll explain it in two steps to answer your two main questions.
Q1: What is meant by "partial irreversibility of the bonding force?"
All bonding, including the bonding responsible for friction, is due to electrostatic attraction between atoms. Here is what that looks like for Hydrogen:


Image source: Chemistry 301, University of Texas (online resource) 

As the two hydrogen atoms approach each other from very far apart, they experience an attractive force until they reach the minimum of the potential energy "well." At this point they experience a repulsive force if they move any closer together. Once the atoms have reached the most stable state it requires additional force to disturb the system, which is the "irreversibility of the bonding force." As two surfaces slide by each other, bonds are being continuously broken and formed in a periodic fashion.
Q2: What does "irreversibility" have to do with friction?
In the Prandtl-Tomlinson model, the force resisting two surfaces moving past each other is modeled as a ball (point mass) climbing up a series of hills due to a horizontal force marked F:

The model helps explain some features of macroscopic friction, such as why there is "static friction" vs. "kinetic friction" -- it takes a little extra force to get the ball moving at first. In the model (details below the jump), increasing the force squeezing the two surfaces together increases the height of the hill. The irreversibility has to do with the fact that it is easier for the ball to roll down the hill than roll up it, and the "degree of irreversibility" is increased if the height of the hill is increased. It is just a model of friction, because friction itself is very complicated. The source you cite connects the irreversibility of bonding and the irreversibility in the Prandtl-Tomlinson model, but that is not stated explicitly in any reference I have access to.

For the curious, here are the details of the Prandtl-Tomlinson model, from an article published by the Technical University of Berlin:

A: It means (havent read the theory) that since friction is not conservative force (dissipative, irreversible), i.e if one drags an object in the opposite direction there is not "negative" friction that actually accelerates, friction in any direction dumps the motion, this is a form of dissipation or irreversibility.
And this friction irreversibility is connected to another irreversibility of atomic bonds, i.e it is easier to make bonds (and adhere) than unmake them (stick versus unstick)
Friction is assumed to be due to atomic interactions between the surfaces of the objects that are moving relative to each other.  These atomic interactions (i.e bonds) and their irreversibility is taken as the prior cause of the phenomenological (manifested) irreversibility of the macroscopic effect called friction.
