PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
April 25, 20260 citationsOpen Access

TERM: Spectral Relaxation and the Entropic Arrow of Time in Variational Systems

View Full Paper
SDSteve Van Dessel

Key Points

  • The aim is to establish a spectral formulation of time in variational systems that encapsulates stability and entropy.
  • Developed a spectral approach to time in variational systems.
  • Analyzed stability along minimizing paths using the Jacobi operator.
  • Derived local rates of entropic time and identified spectral bottom as a temporal inertia scale.
  • Demonstrated that smoothing deformations lower the spectral bottom, affecting entropy.
  • Defined an intrinsic entropic arrow of time based on monotonicity of the spectral entropy functional.
  • Provided background on the ζ-determinant and the min–max principle in appendices.

Abstract

This work develops a spectral formulation of time in variational systems. Stability along minimizing paths is encoded in the Jacobi operator, and smoothing deformations are shown to lower the spectral bottom, inducing a strictly monotone increase of a ζ-regularized spectral entropy functional. This monotonicity defines an intrinsic entropic arrow of time. The paper derives the local rate of entropic time and identifies the spectral bottom as an intrinsic temporal inertia scale. Appendices provide background on the ζ-determinant and the min–max principle.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Steve Van Dessel (2026) studied this question.

synapsesocial.com/papers/69ec5b0688ba6daa22dac931https://doi.org/10.5281/zenodo.19709933
Ask AI
Helpful
Bookmark
Share
View Full Paper