State-transition structures in physics and in computation

In order to establish close connections between physical and computational processes, it is assumed that the concepts of state and of transition are acceptable both to physicists and to computer scientists, at least in an informal way. The aim of this paper is to propose formal definitions of state and transition elements on the basis of very low level physical concepts in such a way that (1) all physically possible computations can be described as embedded in physical processes; (2) the computational aspects of physical processes can be described on a well-defined level of abstraction; (3) the gulf between the continuous models of physics and the discrete models of computer science can be bridged by simple mathematical constructs which may be given a physical interpretation; (4) a combinatorial, nonstatistical definition of information can be given on low levels of abstraction which may serve as a basis to derive higher-level concepts of information, e.g., by a statistical or probabilistic approach. Conceivable practical consequences are discussed.