In static analysis of forces you can in fact have an irreversible couch/sofa event (as in Dirk Gently's ). It is usually is described as jamming or wedging of the peg in hole problem (see here http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/ol... ) and arises when the implied forces can oppose any force to move the object. In this model you can stick a peg in at the wrong angle and it will jam and never come out.
I ran into this when I tried to explain the sofa stuck in the staircase mystery in Dirk Gently's Holistic Detective Agency. She (a Ph.D. in robotics specializing in dynamics and physics) pointed out an idealized rigid system could jam in this way without any additional exotic explanation (beyond the exoticness of idealized rigid physics).
Is this simply because the coefficient of friction between two surfaces is typically smaller when the surfaces are in motion than when they are at rest? If you wanted to reverse the insertion of a peg into a hole, you would have to halt it's motion for an instant, and at that point in time I would imagine you have to overcome static friction to make it move in the opposite direction. Friction forces can be dependent on the normal force between the two surfaces, so it's possible to jam a peg into a hole so that you can't get it out.
Unfortunately it is merely a math problem. Until the peg comes in contact there is no friction. After it is in contact there is friction, and if the geometry is just wrong enough "virtual forces" to oppose any force. Real matter (which bends) can't have this problem- it is from the rigid model. The non-reversaiblity is this flaw plus the fact there is no friction in the model prior to contact (so there is a non-reverisble feature in the model).
It makes sense. After all, in real life I would just wiggle the peg to "walk" it back out of the hole, and that only works if the body is not perfectly rigid, and no body is perfectly rigid.
I'm currently repairing some 1940s windows and replacing the hinges. I can say with confidence that some things are completely rigid and will never be moved despite use of hand and power tool. Old hardwood and steel construction.
I'm rather surprised that an idealised system isn't simply time-reversible, given the trouble physicists had in developing entropy to explain the arrow of time in the first place.
Edit: ah, you've explained below that the model includes a non-reversible term of friction which is applied at the time of contact.
But your original feeling is right- most complete models are in fact time reversible. The static analysis toolkit is a simplified physics for engineering analysis.
IIRC, in Dirk Gently's, the couch wasn't jammed, it was simply that there was no way in which it could be rotated that would allow it to progress either further up the stairs or back down the stairs.
I ran into this when I tried to explain the sofa stuck in the staircase mystery in Dirk Gently's Holistic Detective Agency. She (a Ph.D. in robotics specializing in dynamics and physics) pointed out an idealized rigid system could jam in this way without any additional exotic explanation (beyond the exoticness of idealized rigid physics).