Quantum Coherence and Phase Ontology: Empiricizing the Improbable through Resonant Computation

Hidehito KOBAYASHI

This note proposes a measure-theoretic reinterpretation of observation andmathematical structure. Revisiting the early modern distinction between primary and secondaryqualities, it argues that this division reflects not an ontological boundarybut the historical availability of stabilized measures.Mathematics itself is shown to have aligned, often tacitly, with perceptualmodes that had already acquired measure. From this perspective, Fourier and Laplace analysis are reinterpreted asmeasure-calibrated observational devices operating through push–pull dynamics,rather than as decompositions of physical reality.Hilbert space is positioned not as an ontology of states but as a stabilizationapparatus for probabilistic observables under normalization constraints. Quantum-mechanical notions such as “flavor” are discussed as emblematic markersof distinctions that are observable and transformable yet not fully measurable. The note is exploratory and conceptual in nature.Its aim is to reposition measure theory as a foundational theory of observationitself, connecting empiricism, mathematical structure, and probabilisticphysics within a unified generative framework.

Jeeva S. Anandan, John L. Safko

Andrei T. Patrascu

Quantum coherence profoundly alters classical thermodynamic expectations by modifying the structure and accessibility of probability distributions. Classically, transitions to lower-entropy states (local second-law violations) are exponentially suppressed, as lower-entropy configurations have fewer available microstates and are statistically improbable. However, introducing quantum coherence and structured quantum interference among semiclassical trajectories significantly changes this scenario. Quantum coherence reduces local entropy by establishing correlations among states that are classically independent, effectively restructuring probability amplitudes to channel transitions toward otherwise improbable low-entropy states. We analyze this phenomenon explicitly within the framework of semiclassical approximations, employing the Van Vleck-Gutzwiller propagator to quantify how interference terms arising from coherent superpositions modify classical fluctuation theorems. We demonstrate that quantum coherence, especially when combined with chaos-assisted dynamical tunneling, greatly enhances the probability of transitions to low-entropy configurations, creating pronounced counter-ergodic effects. Furthermore, by considering purification of mixed quantum states, we propose methodologies for deliberately engineering quantum phases among interfering pathways. This phase engineering can explicitly enhance coherence-driven transitions into lower-entropy states, providing a novel thermodynamic resource. Finally, we explore the feasibility of molecular-scale quantum machines exploiting these principles, highlighting their potential applications in quantum thermodynamics and quantum biology for performing useful work through coherence-mediated entropy reduction.

Miguel Orszag

Certain difficult computational problems, such as finding prime factors, could be performed much faster if quantum computing, in which interactions of pure quantum states correspond to logical operations, could be realized in a practical manner. Most schemes implemented or proposed require isolating or controlling single atoms to maintain the coherence of quantum states. Gershenfeld and Chuang (p. 350; see the news story by Taubes, p. 307) propose a different approach in which the manipulation of nuclear spins in a chemical compound with nuclear magnetic resonance (NMR) methods performs quantum computation. Such an approach might seem improbable in that the nuclear spins of a bulk sample form a statistical ensemble that would rapidly undergo decoherence. However, the authors show that the deviation from the equilibrium spin states can be manipulated so that it acts like a pure, low-dimensional quantum state.