  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.
