Towards a Fourth Law: Point 1

Abstract

Towards a Fourth Law: Point 1 - Conservation Derived from a Vacuum Duality Principle This work presents Point 1 of a research program aiming to derive thermodynamic laws from first principles. We do not claim a fourth law here. We introduce two complementary vacuum volumes: - Anergy: V_AV - Exergy: V_EX Total volume: V_tot = V_AV + V_EX Vacuum duality: B_AV = V_AV - V_EX The geometric volume is a^3, where a is the scale factor. Point 1 assumes conservation: Vdot_tot=0 under conditions derived from B_AV dynamics. The dynamical law is: Vdot_tot = 2 V_tot * (Bdot_AV / B_AV) , B_AV ≠ 0 (Option A: singular condition) Vdot_AV = 1/2 (Vdot_tot + Bdot_AV) Vdot_EX = 1/2 (Vdot_tot - Bdot_AV) Requirements: - Exergy: Vdot_EX > 0 implies growth - Anergy: Vdot_EX > 0 acts as a dynamical requirement (not an unconditional identity), consistent with V_tot conservation We define vacuum density rho_vac and pressure p_vac from V_AV, V_EX, B_AV, and show compatibility with H = adot / a. Figures are schematic (arbitrary units), not fits to data. Keywords: vacuum duality, anergy, exergy, fourth law, cosmology, thermodynamics, conservation law, scale factor, V_tot, B_AV Notes: Author: Igor Rant Marušič, ORCID: 0009-0002-0721-3554. Independent researcher. No conflict. No funding.