Chaos, Fractal in Biology, Biothermodynamics and Matrix Representation on Hypercycle

Abstract

First, we discuss biofield and some nonlinear theories in biology. Next, chaos in biology and its application to cancer are researched. Third, fractal and complex dimension in biology are searched. Fourth, nonlinear biothermodynamics and in which possible entropy decrease are investigated. Fifth, we propose the matrix representations of hypercycle theory. Hypercycle can be defined by a degree of connectivity. Its fuzzy element corresponds to that each element is fractal. NeuroQuantology should be nonlinearity and quantization, and may relate to quantum chaos, quantized matrix, etc.

Thermal degradation of mango (Mangifera indica) wood sawdust in a nitrogen environment: characterization, kinetics, reaction mechanism, and thermodynamic analysis

“…After the above conversion range, the system entropy decreases up to a conversion value of 0.65 (384 °C), which is indicative of the association of small molecules to form product molecules within the reactive system. 44 This is consistent with the decrease in Δ H α values that show a decrement in endothermicity of the reactive system. This supports the fact that in this region the entropy of the system decreases due to the dominance of reaction in which association of molecules takes place.…”

“…It is a fact that if A α < 10 9 min −1 , it is considered as low and often indicates less surface reactivity of the system. 44 In present case, higher A α values were noticed for 0.3 ≤ α ≤ 0.5 (from 8.5 × 10 13 min −1 to 2.1 × 10 15 min −1 ), which corresponds to the temperature range of 326–350 °C, indicating high surface reactivity of MIW particle along with formation of a simple activated complex. 45 From Fig.…”

Biological Lattice Gauge Theory as Modeling of Quantum Neural Networks

“…(9) When the complex dimension is combined with relativity, whose dimensions are three real spaces and one imaginary time, it expresses a change of the fractal dimension with time or energy, etc. It exists widely in biology [39]. We discussed their existence in the fractal's description of meteorology, seismology, medicine and the structure of particle, etc [36,38,39].…”

“…It exists widely in biology [39]. We discussed their existence in the fractal's description of meteorology, seismology, medicine and the structure of particle, etc [36,38,39].…”

“…We proposed the matrix representations of hypercycle theory. The quantum neural biology should be nonlinearity and quantization, and may relate to quantum chaos, quantized matrix, etc [39]. The matrix formulation is also a form of quantum mechanics, and is related with quantum biology and neural biology.…”