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

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.