Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2025
|
| Online Access: | https://doi.org/10.5281/zenodo.17165753 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- <p>This paper reveals and proves a profound mathematical identity between the dynamical evolution of physical systems (governed by the principle of least action) and the perceptual inference of cognitive systems (governed by predictive error minimization). This identity arises from two more fundamental physical principles: time-translation symmetry (energy conservation guaranteed by Noether's theorem) and asymptotic stability of equilibrium states. We prove that these two principles jointly require that the linear response function of any system near equilibrium must be completely monotone. Applying Bernstein's theorem, this response function can necessarily be represented as a superposition of exponentially decaying modes with non-negative weights, i.e., the system possesses an orthogonal spectrum of relaxation modes. This result indicates that “minimizing action” and “minimizing predictive error” are, respectively, the physical and cognitive realizations of exponential relaxation toward a stable equilibrium. As a direct and important application of this unified framework, we apply it to cosmology and show that, by analyzing the linear response of the cosmic energy density to perturbations, the unique condition for maintaining the stability of the vacuum state requires the dark energy equation of state parameter to be w=-1. This provides a first-principles, inevitable explanation for the cosmological constant, beyond any previous model-dependent argumentation.</p>