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Springer eBooks

Towards a Process Formalism in Quantum Physics

Clive W. Kilmister

Published Jan 1, 1988• 1 citation
Publisher
DOI
10.1007/978-94-009-2925-8_12

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A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating $S(f) \sim 1/f^α$, thus offering a biophysical explanation for the ubiquitous $1/f$-type in neurological signals.

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The Formalism of Quantum Mechanics

Y. B. Band, Y. Avishai

Elsevier eBooks•Dec 14, 2012•4 citations
Vladimir Lerner’s Information Macrodynamic (IMD) formalism is the first full application of John Archibald Wheeler’s “It from Bit” approach to physical Information processes. The IMD formalism accounts for the evolution of Information physics from quantum to classical regimes, showing how intelligence and Wheeler’s Observer-Participator are naturally emergent. Distinct from “digital physics” or simple coding-decoding schemes, the IMD formalism presents a continuous step-by-step physics of natural Information processes, from the first distinction to the emergence of the self-aware Information Observer.
This work develops a process–event ontological framework for quantum theory, with particular emphasis on information, collapse, and the energetic cost of realization. The central claim is that quantum mechanics formally describes physical processes—coherent, continuous, and reversible in principle—while information, records, and outcomes arise only at the level of events, through irreversible physical realization. Within this framework, collapse is redefined not as a dynamical anomaly, but as the physical realization of a process into an event. Information is not treated as a primary entity or carrier, but as a stabilized physical imprint of events, necessarily involving energy dissipation. The framework reinterprets Landauer’s principle as a cost of record stabilization rather than bit erasure, clarifies the ontological status of qubits as energetically maintained process states, and resolves standard measurement paradoxes without modifying the formalism of quantum mechanics. This work operates at a meta-level: it does not propose new dynamics or interpretations, but explicitly delineates the boundary between quantum processes and realized events.
A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating S(f)∼1/fαS(f) \sim 1/f^αS(f)∼1/fα, thus offering a biophysical explanation for the ubiquitous 1/f1/f1/f-type in neurological signals.