Entropy-Corrected Schr¨odinger Dynamics from Quantum Causal Entropy Theory

Standard quantum mechanics describes the evolution of physical systems through unitary Schr¨odinger dynamics, while decoherence and wavefunction collapse are introduced through additional postulates or environmental interactions. Although highly successful operationally, the theory does not provide a fundamental dynamical mechanism explaining the emergence of classical localization from microscopic evolution. n this work we propose an entropy-weighted causal dynamics framework, referred to as Quantum Causal Entropy (QCE), in which each microscopic causal transition contributes both a phase increment and an entropy cost. Starting from a local causal update rule, Ψ → eiθℓ−∆SℓΨ, we derive a modified evolution equation in which the standard Hamiltonian generator is supplemented by an entropy-production operator. The resulting entropy-corrected Schr¨odinger equation takes the form iℏ dΨ dt =H − iℏλSˆΨ, where Sˆ represents the entropy rate associated with microscopic causal processes and λ is an entropy coupling constant. We show that the standard unitary Schr¨odinger evolution is recovered in the limit of vanishing entropy coupling, while finite entropy production leads naturally to decoherence, interference suppression, and effective measurement localization without invoking an explicit collapse postulate. A corresponding density-matrix evolution equation is derived, providing a thermodynamic description of coherence decay. The framework therefore provides a dynamical link between quantum evolution, information entropy, and emergent classicality, and suggests experimentally testable corrections to coherence behavior in controlled quantum systems