they possess a measurable size
- Is this statement generally accepted,
The statement describes what is observed experimentally. The main interactions in keeping the proton as a particle with a given mass composed of quarks are the electromagnetic and the strong, whose balance, one attractive (strong ) one repulsive (electromagnetic) define the bound state of a proton, quantum mechanically . This is modeled in various ways and the models are validated with new experiments. Quantum mechanics is essential for modeling mathematically the microcosm of particles.
suggesting that quarks are not measurable in size?
It does not suggest that, though as far as QM modeling goes, all elementary particles, including quarks, are axiomatically assumed to be point particles.
- If a proton has a radius, does it necessarily have a surface, and, in particular, a surface that might be described by the thermodynamics of surfaces?
One cannot apply classical mechanics theories, as thermodynamic surfaces, to quantum mechanical entities. Quantum mechanics is a probabilistic theory, giving the probability of interaction. In the case of the proton, when it interacts with a charged particle the spill over charges of the quarks inside will interact with it , either attractively or repulsively . For a group/gas of protons, they will interact repulsively to each other when at low temperatures, and this repulsion will define statistically a surface for the proton. Depending on their energy the interaction starts seeing the individual quark-quark scatters, as at the energies of the LHC
Because protons are not fundamental particles, they possess a measurable size; the root mean square charge radius of a proton is about 0.84–0.87 fm
This radius defines a type of surface but it certainly has nothing to do with thermodynamic classical concepts.