Bits, Cobits, and Qubits: Partial Coherence in Dissipative Systems

Background: Information theory has traditionally centered on two paradigms: classical bits (completely decoherent states) and quantum qubits (fully coherent states). However, many complex adaptive systems—particularly biological neural networks—operate in an intermediate regime characterized by partial coherence maintained through continuous entropy gradients. Purpose: We introduce ”cobits” as a novel information measure quantifying partial coherence in dissipative systems, addressing a fundamental gap between classical and quantum information theories. Theory: Cobits are mathematically formalized through a coherence measure C(ρ) and a newly introduced smoothness parameter Γ, where Hcobit(ρ,Γ) = Γ·C(ρ) log2(Deff). The Γ parameter explicitly quantifies the continuity of entropy flow, differentiating dissipative coherent systems from both classical and quantum extremes. Key Insight: Cobit-based coherence is inherently resistant to reductionist measurement approaches, as measurement disrupts the continuous entropy gradients that sustain partial coherence. Results: Biological neural networks function as high-Γ cobit systems, with ephaptic fields and neural criticality serving as mechanisms that smooth discrete entropy inputs into continuous coherence, explaining why reductionist approaches to neuroscience often fail to capture emergent cognitive phenomena. Conclusions: The bit-cobit-qubit spectrum provides a unified framework for understanding information processing across disparate systems, with profound implications for neuroscience, artificial intelligence, physics, and complex systems theory more broadly.