Fluctuations and Long-Term Stability: from Coherence to Chaos

Abstract

Exerting fluctuations is a part of our daily life: traffic noise, heartbeat, opinion poll, currency exchange rate, electrical current, chemical reactions - they all permanently fluctuate. One of the most important questions is why the systems that exert fluctuations stay long-term stable. Is there any general functional relation that provides long-term stability despite the wide diversity of the fluctuations commence: emotions, economics, physical interactions etc? I assert that such functional relation does exist and reveal its specification: the route to the long-term stability is through coherence and boundedness as necessary conditions. It is demonstrated that the chaoticity is the hallmark of that relationship. The present contribution is a systematic study written as a book on the relation between long-term stability and exerting macroscopic fluctuations. Further attention is focused on the mechanism that guarantees the boundedness and the coherence of the local fluctuations in the physical systems. Crucial arguments that neither of the existing so far approaches to the behavior of the extended many-body systems provides boundedness and coherence of the fluctuations are put forward. It turns out that the mechanism that brings about macroscopic fluctuations has universal properties and entangles quantum decoherence, chaos and 1/f noise in a tricky interplay.