Information and thermodynamics' first law

Thermodynamics' first law (TFL), although undoubtedly true because of its many verified consequences, rests on a rather weak experimental foundation in the sense that, as pointed out by Pippard, its path-independent aspect cannot be said to have been directly verified. From the theoretical side, also questionable is the need of invoking the adiabatic theorem (AT) to prove the TFL from first principles. We provide a more direct theoretical demonstration, derived from information theory, without the AT and some other usually employed arguments.