Comment on Derivatives don't always act like fractions (2021)parentComments−Y_Y1yYou're not, in general, just working in a vector space but on a manifold whose coordinates are your extensive variables. It's only linear locally, in the (co-)tangent space where you're doing calculus.See e.g. https://arxiv.org/pdf/1811.04227Or this Physics SE discussion: https://physics.stackexchange.com/questions/388318/how-exact...
Comments
You're not, in general, just working in a vector space but on a manifold whose coordinates are your extensive variables. It's only linear locally, in the (co-)tangent space where you're doing calculus.
See e.g. https://arxiv.org/pdf/1811.04227
Or this Physics SE discussion: https://physics.stackexchange.com/questions/388318/how-exact...