Solid State Theory Department,

Institute of Metal Physics of NAS of Ukraine,

Prospect Vernadskogo 36,

Kyiv, 03142 UKRAINE

E-mail: kiril@metfiz.freenet.kiev.ua

**Universal symmetry of complexity and its manifestations
at different levels of world dynamics**

**Abstract:**

A universally nonperturbative analysis of an arbitrary interaction
process described by a quite general dynamical equation provides the 'dynamically
multivalued' general solution that contains many equally valid, locally
complete problem solutions representing possible system configurations,
or 'realisations'. This unreduced solution leads to purely dynamical, rigorously
derived (nonaxiomatic) definitons of true randomness, probability, chaoticity,
complexity, nonlinearity and other related properties [1, 2] which extend
considerably their axiomatic introduction in the conventional, dynamically
single-valued theory ('exact solutions' and their 'small perturbations').
Any dynamical system evolution can now be expressed in terms of the absolutely
universal law of conservation, or symmetry, of complexity that includes
extended, universally applicable versions of the 'first' and 'second' laws
of thermodynamics (conservation and degradation of energy, respectively)
and actually any other (correct) dynamical symmetry, law, or 'principle',
governing real system development. We demonstrate particular manifestations
of this universal symmetry at various levels of world dynamics [1, 2],
including causally complete, intrinsically unified explanation of 'quantum
mysteries' and 'relativistic' effects [3], purely dynamic origin of (true)
quantum and classical chaos related by the ordinary correspondence principle
[4], extended, dynamically probabilistic fractals and their applications
in biology and medicine [5].

**References**

- A.P. Kirilyuk, "Universal Concept of Complexity by the Dynamic Redundance Paradigm: Causal Randomness, Complete Wave Mechanics, and the Ultimate Unification of Knowledge" (Naukova Dumka, Kiev, 1997), 550 p., in English. For a non-technical review see also physics/9806002
- A.P. Kirilyuk, "Dynamically Multivalued, Not Unitary or Stochastic, Operation of Real Quantum, Classical and Hybrid Micro-Machines", physics/0211071
- A.P. Kirilyuk, "Universal gravitation as a complex-dynamical process, renormalised Planckian units, and the spectrum of elementary particles", gr-qc/9906077
- A.P. Kirilyuk, "Quantum chaos and fundamental multivaluedness of dynamical functions", Annales de la Fondation Louis de Broglie, v. 21 (1996) 455; quant-ph/9511034
- A.P. Kirilyuk, "The Universal Dynamic Complexity as Extended Dynamic Fractality: Causally Complete Understanding of Living Systems Emergence and Operation", In: "Fractals in Biology and Medicine", Vol. III, ed. by G.A. Losa, D. Merlini, T.F. Nonnenmacher, and E.R. Weibel (Birkh?user, Basel, 2002), p. 271.