Computational Description of Physical Systems

Abstract This chapter introduces computational descriptions of physical systems (CDPSs), which are physical descriptions of physical systems (PDPSs) that map onto abstract computational definitions of computing systems (CDCSs) via physical-to-computational mappings (PCMs). Physical-to-computational mappings are dynamically self-consistent mappings from some or all elements of a PDPS to all elements of a CDCS, where dynamical self-consistency requires that the transformations of all computationally relevant physical states conform to the transformations of the computational states onto which they map. This minimal notion of a CDPS will be placed in the context of stronger alternatives in Chapter 4, where minimal qualifying criteria that any CDPS must satisfy are supplemented by additional criteria that give rise to stronger classes of CDPSs. The classification of CDPSs by the restrictiveness of the strength criteria they satisfy provides a useful and transparent strategy for evaluating claims that particular physical systems implement particular computations.