Spacetime differential elements and the distribution of bio-Hamiltonian components

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Various Hamiltonian models have been derived for chemical structures belonging to living organisms while the Hamiltonian concept was not applied to life as a whole. However, Hamiltonian components were recently defined for living organisms on the condition to take in consideration their evolutionary implications (Bounias, 2001: CASYS'0l). This paper identifies differential elements of Spacetime, from which it delimits a probabilistic fuzzy-like invariance standing for conservativity of biological Hamiltonians. The distributions of potential and kinetic components in a individual bio-Hamiltonian, and the distribution of such individual Hamiltonians of living organisms interacting in more complex systems are shown to behave as a non-linear generalized convolution of functions.