Holographic principle tells why maximum entropy principle, lognormal distribution, self-preserving and self-organization appearing in system evolutions across science

TL;DR

This paper uses the holographic principle and information entropy to explain why systems across science tend to evolve towards patterns like maximum entropy, power laws, and self-organization, supported by theoretical derivations and simulations.

Contribution

It introduces a novel mechanism linking holographic principle with system evolution patterns through maximum information entropy principle and information entropic force.

Findings

Self-preserving and lognormal distributions are caused by MIEP.

Particle system evolution is driven by information entropic force (Fient).

Quantum wave functions also satisfy MIEP.

Abstract

By applying the holographic principle that comes from black hole physics and information entropy (Sient) introduced by Claude Shannon, we derive the mechanism of similar patterns or tendencies appearing in evolution processes of different systems: maximum entropy principle, power law and lognormal distributions, self preserving and self organization. Taking a system of atmospheric particles as an example, we prove both self preserving and lognormal distribution patterns are caused by maximum information entropy principle (MIEP); By deducing thermodynamic entropy (Stent) is a form of Sient, and building up a particle system approaching a part of the holographic screen, the information probability statistics of particle number size distribution are realized on the holographic screen, resulting in the presence of information entropic force (Fient). Fient drives the system to evolve in the direction of MIEP. Owing to the initial state, the evolution can undergo an increasing Sient and enhanced discretization, or a decreasing Sient and weakened discretization. The latter process corresponds to the system evolution tendency of self organization; by introducing Fient into the flow field, the field for fluid system evolution is unified including Fient, Sient, the Newton potential, the diffusion process, and Navier Stokes equations, indicating that the atmospheric particle dynamics could be driven by Fient. By numerical simulations of particle collisions and coagulation based on the Smoluchowski equation, we prove the evolution of the particle system is indeed information distributing, inherited from the initial state, measured by information probability, evaluated by Sient, and driven by Fient. We further prove wave function for quantum mechanism also satisfies MIEP. The findings indicate holographic principle can guide system evolution towards certain desirable patterns and outcomes.