Information-Entropy Evolution and the Emergence of Time: A Fundamental Constitutive Relation for Local Intrinsic Time

Whether time possesses an ontological status independent of physical-state evolution remains an open question in foundational physics. We propose a fundamental framework in which a local intrinsic time scale τ emerges as a direct consequence of information-entropy evolution. We demonstrate that in the absence of an absolute background clock, time must be defined operationally through internal state transitions. By identifying information entropy as the unique measure of state distinguishability and irreversibility in probabilistic dynamics, we propose the constitutive relation dτ = α dSlocal. Motivated by the Kubo Martin-Schwinger (KMS) condition and Wick rotation, we scale the factor as α = ℏ/(kBT), establishing temperature as the derivative of entropy with respect to intrinsic time: T = (ℏ/kB)(dS/dτ ). Bridging the microscopic and macroscopic realms via the Boltzmann relation, we obtain a parameter-free integral kB 2 ℏ ∆τ = ∫︁ d T Q 2 . The framework yields profound predictions for extreme physical regimes, including a holographic geometric factor (4π) in black hole time dilation, the intrinsic-time freezing at zero temperature, and a discontinuous step-jump in cumulative intrinsic time during the first-order phase transition of real materials. Consistency checks using the quantum Zeno effect and the quantum eraser demonstrate how local entropy suppression and postselected information recovery correspond to dynamical freezing and negative time increments.