Trying to Understand Entropy I'm currently looking at Principles of Chemistry by Atkins, and I have a few questions involving entropy. These questions probably arise from my poor understanding of reversible/irreversible processes.


Why are reversible processes called reversible? Is it necessarily true that reversible processes can be reverted spontaneously, or is this a common misconception that people have?
So my chemistry textbook gives the definition of entropy as
$$\Delta S = \frac{q_{rev}}{T}$$
where $q_{rev}$ is heat transferred reversibly. However, I get lost at how entropy could increase during a reversible process.
Why is the reversibility condition necessary for the definition of entropy?
They're called "reversible" because the processes can run backwards without additional input of energy. There aren't really any truly reversible processes in the universe, though (some come very close, but the construct of "reversible" is an ideal, not a reality).
Entropy of a system can increase just fine during a reversible process: expanding a gas "slowly enough" is reversible ("slowly enough" means in an infinite number of infinitesimal steps), but the entropy of the gas increases as it expands as it has more microstates to go into. The entropy that remains constant in a reversible process is that of the system plus the surroundings (in other words, the universe).
The process does not need to be reversible to have entropy. However, we measure entropy based on the heat of the reversible process because entropy is a state function (it depends on the beginning and end points of your process, nothing more) while heat is a path function (it depends on the path you take to get there).