Recurrence Resonance and 1/f Noise in Neurons Under Quantum Conditions and Their Manifestations in Proteinoid Microspheres

Recurrence resonance (RR), in which external noise is utilized to enhance the behaviour of hidden attractors in a system, is a phenomenon often observed in biological systems and is expected to adjust between chaos and order to increase computational power. It is known that connections of neurons that are relatively dense make it possible to achieve RR and can be measured by global mutual information. Here, we used a Boltzmann machine to investigate how the manifestation of RR changes when the connection pattern between neurons is changed. When the connection strength pattern between neurons forms a partially sparse cluster structure revealing Boolean algebra or Quantum logic, an increase in mutual information and the formation of a maximum value are observed not only in the entire network but also in the subsystems of the network, making recurrence resonance detectable. It is also found that in a clustered connection distribution, the state time series of a single neuron shows $1/f$ noise. In proteinoid microspheres, clusters of amino acid compounds, the time series of localized potential changes emit pulses like neurons and transmit and receive information. Indeed, it is found that these also exhibit $1/f$ noise, and the results here also suggest RR.