Energy Conservation Through Universal Entropic Frequency Transformation in Extended Classical Mechanics

 Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | July 18, 2026

Within the framework of Extended Classical Mechanics (ECM), dark energy represents latent potential energy, while its manifested kinetic counterpart is the effective antigravitational interaction responsible for the expansion of the material universe.

According to observational cosmology, particularly studies of the Coma Cluster, the effective gravitating mass is expressed as

Mɢ = Mᴍ + Mᴅᴇ

where

Mᴍ = Mᴏʀᴅ + Mᴅᴍ

is the total matter component (ordinary matter plus dark matter), and Mᴅᴇ is the effective negative-mass contribution associated with dark energy.

In Extended Classical Mechanics, the corresponding relation is

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ

which directly identifies the dark-energy contribution as

Mᴅᴇ = −Mᵃᵖᵖ.

ECM further interprets this relationship through the universal entropic transformation

f₀ = fᴘ + Δf₀ → fꜱᴏᴜʀᴄᴇ = fᴏʙꜱᴇʀᴠᴇᴅ + Δfꜱᴏᴜʀᴄᴇ

where the latent energy represented by −Mᵃᵖᵖ corresponds to the phase-dependent frequency components Δf₀ and Δfꜱᴏᴜʀᴄᴇ. These frequency differences describe the continuous transformation between the latent source state and the manifested observable state.

Consequently, the apparent increase in observable energy during cosmic expansion does not represent the creation of energy from nothing. Rather, it reflects the continuous phase-dependent transformation of latent potential energy into manifested physical energy while preserving the total energy of the system. Within ECM, energy conservation is therefore maintained through the entropic frequency transformation linking f₀, fᴘ, fꜱᴏᴜʀᴄᴇ, and fᴏʙꜱᴇʀᴠᴇᴅ.