Mathematical Formalization of Cobits: Technical Note Thermodynamic Coherence and the Origins of Quantization

This technical note provides a rigorous mathematical foundation for the cobit framework introduced in “Bits, Cobits, and Qubits: Partial Coherence in Dissipative Systems.” We formalize cobits using complex number representation, define entropy flow continuity in terms of phase stability, and establish a thermodynamic basis for quantization. This mathematical formalization demonstrates how cobits bridge classical and quantum information while providing a framework for analyzing partially coherent states maintained by continuous entropy flow in dissipative systems.