In this video we show that the geometry of states in both classical and quantum mechanics is exactly the structure needed to define the entropy.
The ideas presented are extracted from our research. Papers ( https://assumptionsofphysics.org/papers.html ) and presentations ( https://assumptionsofphysics.org/presentations.html ) available from the project website. For example:
Hamiltonian mechanics is conservation of information entropy ( https://arxiv.org/abs/2004.11569 )
How quantum mechanics requires non-additive measures ( https://arxiv.org/abs/2311.01951 )
The unphysicality of Hilbert spaces ( https://arxiv.org/abs/2308.06669 )