On the Arrow of Time and Organized Complexity in the Universe
Tatsuaki Okamoto
Abstract
There is a widespread assumption that the universe in general, and the Earth's biosphere in particular, is becoming more complex over time. This paper formulates this assumption as a macroscopic law, the law of increasing complexity, for a system over a finite time span. It hypothesizes that this macroscopic law emerges in certain non-equilibrium systems with abundant free energy flows, such as the observable universe and the Earth's biosphere. We distinguish between two types of complexity: disorganized and organized. The complexity associated with this assumption is organized complexity. To formulate this law, we employ a quantitative definition of organized complexity as applied to probability distributions. We represent any object of complexity as the source of its observed value, which is expressed as a probability distribution; this enables a unified treatment of diverse objects. This formulation necessitates the use of observation systems to represent these objects. We introduce an order relation between these observation systems to demonstrate that the complexity of an object possesses a generic property, one that does not depend on any specific observation system. This paper develops a novel methodology for this macroscopic law, which formulates the arrow of time in terms of increasing organized complexity for certain non-equilibrium systems. This contrasts with the second law of thermodynamics, which formulates the arrow of time in terms of increasing disorganized complexity (entropy) for isolated systems. We apply this formulation to the fine-tuning problem: the puzzling observation that the fundamental physical constants appear to be fine-tuned for life on Earth. Our new explanation of the fine-tuning problem posits that these constants are fine-tuned for the emergence of the law of increasing complexity.