The theory Emergent Consumable Time from Entanglement

We present a complete and self-consistent formulation of the Emergent Consum-able Time from Entanglement (ECTE) framework, which unifies thermodynamicemergent time and entropic gravity within a single covariant action. In ECTE,physical time arises from quantum entanglement entropy and is consumable viathermodynamic processes, while gravitational dynamics are modified by entropiccorrections mediated by spacetime elasticity. The theory introduces three addi-tional fields: an entanglement scalar ϕ, a thermodynamic time field Ψ, and anentropic tensor τμν . We provide the full action, derive the field equations, establishstability conditions, and demonstrate that all parameters are well-motivated andconsistent with fundamental principles. The model is then confronted with the lat-est cosmological observations, including DESI DR2 BAO measurements, DES Y6weak lensing data, SH0ES+JWST H0 determination, and stochastic gravitationalwave constraints from NANOGrav and LIGO/Virgo. ECTE successfully alleviatesthe H0 tension to below 1σ and the S8 tension to 1.2σ, while improving the overallfit to the combined data with ∆χ2 = −14.9 relative to ΛCDM, corresponding to astrong preference according to the Akaike Information Criterion.