On a local formalism for time evolution of dynamical systems

TL;DR

This paper introduces a local entropy gradient formalism that unifies the irreversibility of complex system evolution with time-reversible dynamical equations, resolving causality issues and deriving principles of special relativity.

Contribution

It presents a novel local maximization formalism for entropy that addresses inconsistencies in time directionality and causality in dynamical systems, linking to special relativity.

Findings

Resolves conflict between reversible equations and irreversible evolution.

Provides a local entropy maximization principle for complex systems.

Derives basic principles of special relativity from the formalism.

Abstract

The formalism of local maximization for entropy gradient producing the evolution and dynamical equations for closed systems. It eliminates the inconsistency between the reversibilty of time in dynamical equations and the strict direction of irreversible evolution for complex systems, causality contradictions and ambiguity of time flow in different systems. Independently it leads to basic principles of special relativity.