  All current formulations of thermodynamics invoke some form of
coarse-graining or ensembles as the supposed link between their own laws and
the microscopic laws of motion. They deal only with ensemble-averages,
expectation values, macroscopic limits, infinite heat baths, etc., not with the
details of physical variables of individual microscopic systems. They are
consistent with the laws of motion for finite systems only in certain
approximations, which improve with increasing scale, given various assumptions
about initial conditions which are neither specified precisely nor even thought
to hold exactly in nature. Here I propose a new formulation of the zeroth,
first and second laws, improving upon the axiomatic approach to thermodynamics
(Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the
recently proposed constructor theory. Specifically, I provide a
non-approximative, scale-independent formulation of 'adiabatic accessibility';
this in turn provides a non-approximative, scale-independent distinction
between work and heat and reveals an unexpected connection between information
theory and the first law of thermodynamics (not just the second). It also
achieves the long-sought unification of the axiomatic approach with Kelvin's.
