Thermodynamic and information entropies: classical and quantum measures models - pedagogical sophisticated benchmarking for IT students

The thermodynamic and information approaches for the investigation of end-to-end IT based on the laws of classical / quantum information theory and design of robust optimal control processes in non-linear non-holonomic (in general global unstable) dynamic systems are introduced. The new type of soft computing based on genetic algorithms with the fitness function as minimum entropy production rate is presented. Control objects are considered as non-linear dynamic systems that in general case described by essentially non-linear stochastic differential equations with stochastic parameters. The algorithm for the calculation of entropy production rate in control object motion and in control systems is developed. In Part 1 (this part), the interrelation between the Lyapunov function (the measure of stochastic stability) and the entropy production rate (the physical measure of controllability) is investigated. Using this interrelation the following qualitative characteristics and important interrelations are described: stochastic dynamic stability motion (average Lyapunov function), Lyapunov exponent and Kolmogorov-Sinai entropy, the physical entropy production rates, and symmetries group representation in essentially non-linear systems as coupled oscillator models. The results of computer simulation for the study entropy-like dynamic behavior for typical Benchmarks of dynamic systems as Van der Pol, Duffing, Holmes-Rand, coupled oscillators and etc. are presented. In Parts 2 and 3 the application of this approach for the simulation of dynamic entropy-like behavior and optimal control of Benchmarks as two-links manipulator in the robot for service use, robotic unicycle and a suspension system of car under stochastic excitations are presented.