Information and system modelling

In this paper, we first give a clear mathematical definition of information. Then based on this definition of information we consider two routes of system modelling. One route is with stochastic information and the other route is with deterministic information. The route with stochastic information gives the usual information theory where information is carried by random variables or stochastic processes. With this route of stochastic information we can derive quantum mechanics. Then our new feature is the route with deterministic information. We show that with deterministic information we can establish deterministic quantum systems (which are quantum systems with no probability interpretation). From these deterministic quantum systems we can derive the three laws of thermodynamics and resolve the paradox between the second law of thermodynamics and the evolution phenomena of the world. We resolve this paradox by clarifying the relation between Shannon information entropy, Boltzmann entropy and the entropy for the second law. This clarification also solves the negative entropy problem of Schroedinger. These deterministic quantum systems which are established with deterministic information can be regarded as solutions to the the debate between Bohr and Einstein and the measurement problem of quantum mechanics because of their deterministic nature and their quantum structure.