Reversible process, equivalence of two definitions? There are two common definitions of a reversible process:

A reversible processes is quasistatic with no dissipation. 

And

A process where an infinitesimal change in conditions would reverse the direction of the process. 

Is it possible to show the equivalence of these two definitions in the general case and if so how? Also are there any specific cases where the equivalence is easily shown? 
 A: The second definition includes involvement of both the system and the surroundings. For this definition, I like to envision that the surroundings has available the following sets of tools:  


*

*Tiny weights that can be added or removed from a piston, when the piston is at different elevations

*An array of constant temperature reservoirs in a continuous sequence of slightly different temperature.
With these sets of tools, we can reversibly transition a system from one state to another while at the same time allowing the combination of system and surroundings to be returned to the original state with no significant change in anything else.
Consider the quasistatic (reversible) expansion with no dissipation you were describing.  To carry this out, you remove each tiny weight from the piston at a sequence of increasing elevations.  The weights correspond to the surroundings.  To compress the system back to its original state, you gradually place the weights back onto the piston, each at their existing elevations.  This enables both the system and the surroundings to be returned to their original states, without significantly affecting anything else.  Of course, in the limit, the weights have to be infinitecimal in size.
The second definition is what we really mean by reversible, since, in the end, nothing has changed.  However, the first definition can also be used to produce the same change in the system, even though the surroundings may not have been  handled reversibly.  Such a reversible process in which the focus is exclusively on the system irresepctive of how the surroundings is handled is referred to by Moran et al in their book Fundamentals of Engineering Thermodynamics as an "internally reversible process."
