# I Definition(s) of "reversible" -- thermodynamics vs mechanical?

1. Feb 5, 2017

### Stephen Tashi

Is there a definition for "reversible process" that applies to mechanical systems (such as a block sliding down a frictionless inclined plane) that is distinct from the definition of "reversible process" in thermodynamics?

If we apply the thermodynamic definition of "reversible process" to the situation of the block sliding down a frictionless inclined plane (and make the tacit assumption that the material of the block and the material in the plane are in thermal equilibrium) then the fact that block is moving with respect to the plane is irrelevant since we are only considering thermodynamic properties of the materials and no heat is being generated.

The definition of "reversible" process for mechanical systems is often ineffectively explained merely by saying that, in real life situations, mechanical processes are irreversible due to friction. This invites the reader to formulate a "default" definition for a "reversible" mechanical process and to define it as a process where there is no friction. That, in turn, would be consistent with the thermodynamic definition, which focuses on the properties of the materials that make up the mechanical system, not their motion with respect to each other.

However, there is a vague intuitive notion of reversibility for mechanical processes that says the process is reversible if it could go "backwards" in time. For a block sliding down a frictionless inclined plane we could imagine an (equally theoretical) structure consisting of a second frictionless upward sloping plane so the block would run up the upward slope, slide back down and replay its journey on the first inclined plane backward in time. However, unlike the thermodynamic definition of "reversible process" the block's path back to its initial state would not be taking a path through equilibrium states.

2. Feb 6, 2017

### Staff: Mentor

To the best of my knowledge, these two concepts of reversibility are the same. It is also the same basic concept used in reversible computing (i.e., deleting information is related to creation of entropy).

3. Feb 6, 2017

### Stephen Tashi

How disappointing! However, I've found nothing on the web to contradict that. At least there is a concept of "equilibrium" ("no unbalanced forces") that is defined for mechanical systems and is a different concept than thermal equilibrium.

If I happen upon a block with mass 1 kg sliding along a frictionless horizontal surface at a velocity of 8 m/sec, can I compute what its state was 15 seconds ago? For example, do I necessarily know that it got its velocity from sliding down an inclined plane 7 seconds ago ? - and how would adding a little friction change the problem of predicting the past ?

The analysis of such situations depends on how we define the state variables of the process. However, at first glance, the conditions for "reversibility" in "reverse computing" seem to be much more demanding than thermodynamic reversibility.

Expositions of topics that mention "entropy" are often too glib because they don't specify how entropy is to be measured. If "entropy" refers to thermodynamic entropy then we lack any standard definition for the "entropy" of a state that is not in thermodynamic equilibrium. If "entropy" refers to Shannon's measure of information, we need to have a probability distribution defined.

The Wikipedia article you linked says:
I very curious about the claimed "rigorously valid observation". Is it an observed fact or is it a mathematical deduction from a series of definitions that make the "observation" true-by-definition?