On the Continuum Fallacy: Is Temperature a Continuous Function?

Abstract It is often argued that the indispensability of continuum models comes from their empirical adequacy despite decoupling microscopic details modelled physical system. There thus a commonly held misconception temperature varying across region space or time can always be accurately represented as continuous function. We discuss three inter-related cases modelling — in phase transitions, thermal boundary resistance and slip flows show view fallacious on ground system are not necessarily decoupled models. how discontinuities present both data (experiments simulations) phenomena (theory models) discontinuum variation may have greater explanatory power. The conclusions our paper are: a) idealisations indispensable to discontinuous representations work depending context; b) continuously defined function best scientific world; c) its continuity, where applicable, contingent matter. also raise question whether should considered truly de-idealised descriptions phenomena.