[eschewthecashew]

If I am correct in my assumption, by definition, for any reversible transformation, the total entropy change must equal zero (dStotal = 0), as there is no natural direction for change in any equilibrium transformation.  In an adiabatic transformation, the change in entropy of the surroundings is always equal to zero, no? (no heat transfer, only work). How can any adiabatic transformation ever be reversible? Even if work is supplied reversibly, dStotal can never be equal to zero. 

Any input appreciated.

[eschewthecashew]

Okay, so I think I have an answer....
My assumption was that, during an adiabatic transformation, since volume increases, the entropy of the system increases....WRONG! Though, the volume increases, since no heat can be supplied from the surroundings, the temperature decreases; these to processes essentially cancel one another out, and the change in entropy of the system is also equal to zero, therefore dstotal = 0.

This means that for any adiabatic transformation, the change in entropy is always equal to zero.

is this logically sound?

[Yggdrasil]

Yes.  Reversible adiabatic transformations are often referred to as isentropic, because they involve no change in entropy.

[eschewthecashew]

Yes.  Reversible adiabatic transformations are often referred to as isentropic, because they involve no change in entropy.

Under what conditions do you then have an irreversible adiabatic transformation?

[Yggdrasil]

A common example of an irreversible adiabatic transformation is the expansion of a gas into a vacuum (an adiabatic free expansions).  I may try to look up a better reference, but this is the only semi-decent discussion I've found on wikipedia during a brief search (http://en.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect)