Cobits: Bridging Classical and Quantum Information for Dissipative Systems

Classical information theory (bits) and quantum information theory (qubits) represent extremes—complete decoherence versus perfect coherence—leaving a gap in describing partially coherent states maintained through continuous entropy exchange. We introduce the Coherence Equation H = Γ·C(ρ)·log2 Deff as a fundamental measure of maintained coherence capacity in thermodynamically open systems, where entropy flow continuity Γ, coherence degree C(ρ), and effective dimensionality Deff quantify structured uncertainty. We define ’cobits’ as systems operating in the regime where H ≥ 1 under dissipative conditions—representing a distinct information processing paradigm where coherence is actively sustained through entropy flow, rather than isolated or resolved. The Coherence Efficiency η= H/∆S characterizes how effectively systems sustain coherence per unit entropy export. This framework extends Landauer’s principle to continuous processes, bridges classical and quantum information theories, explains biological coherence maintenance, and predicts logarithmic scaling of metabolic energy with coherence degree in high-continuity systems.