Universal Dynamical Template Equation Across Disciplines: A Unified Framework of Energetic Deviations
Authors/Creators
Description
This preprint introduces a universal dynamical equation of the form
a(X,t)X'' - b(X,t) X' + c(X,t)X^n = S(X,t)
which captures the evolution of diverse systems by modeling how deviations from equilibrium states act as forces that drive system dynamics.
The variable \(X\) represents a generalized energy-like quantity, while \(S(X,t)\) models destabilizing influences or stimuli. This framework is demonstrated to be applicable across physical, biological, psychological, economic, and literary domains, offering a unified structure to describe dynamic transitions in both the sciences and humanities.
The paper includes illustrative tables that map components of the equation to different disciplines and explains how emotional dynamics in literature, market behavior in economics, and homeostasis in biology can all be described using the same formalism.
This interdisciplinary approach aims to foster a common language for systemic change, revealing deep analogies across seemingly disparate fields.
Keywords:
Dynamical systems, Interdisciplinary modeling, Literary dynamics, Energy deviation, Universal equation, Cross-domain formalism, Mathematical humanities, Social dynamics, Emotional oscillations
Author:
Takashi Ueda
Independent Researcher
ue1119mo0413@gmail.com
Contributions:
Includes structural analysis and interdisciplinary modeling contributions by ChatGPT (OpenAI).