What kind of differential does the small Greek delta letter represent?

[swampwiz]

δ

I had always thought that it represents a differential element for a parameter that it is not supposed to be a well-defined function - e.g., for a differential or heat or work in thermodynamics - as opposed to a regular Latin d, which is supposed to be such a well-defined function. However, Sabina Hossenfelder says here that it means a differential that is meant to be a function whose input variable is a path, which sounds like something out of calculus of variations.

 

[DrClaude]

And I always thought that $\delta$ was Dirac's delta

The same symbol can have different meaning in different contexts.

 

[fresh_42]

δ

I had always thought that it represents a differential element for a parameter that it is not supposed to be a well-defined function - e.g., for a differential or heat or work in thermodynamics - as opposed to a regular Latin d, which is supposed to be such a well-defined function. However, Sabina Hossenfelder says here that it means a differential that is meant to be a function whose input variable is a path, which sounds like something out of calculus of variations.

Here is an example that fits into the context:
https://www.physicsforums.com/insights/when-lie-groups-became-physics/
It is basically how it was used in:
A. Cohen, An Introduction to Lie Theory of One-Parameter Groups, Baltimore 1911

At least, it shows that "something small" is the answer in the given context.