  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 $S(f) \sim 1/f^\alpha$, thus offering a biophysical explanation
for the ubiquitous $1/f$-type in neurological signals.
