We first review the initiation by two of us (R. M. S. and T. V.) [1] of the mathematical representation of life, intended as the difference between organic and inorganic molecules, via the Lie-admissible hyperstructural branch of hadronic mechanics representing the size of biological molecules, their contact thus non-Hamiltonian interactions and the irreversibility over time. We then review and expand the studies done in the subsequent paper [2] showing that: 1) The time irreversible hadronic representation of life can be obtained via the addition of the symmetric Jordan brackets to reversible quantum mechanical Lie brackets; 2) The Lie and Jordan admissible axiomatic formulation of hadronic medicine with non-linear, non-local an non Hamiltonian entanglements of molecular constituents operating without the use of a known form of energy; 3) The smooth connection between hadronic uncertainties at small distances and full Einsteinian determinism at classical distances; 4) The quantitative representation by hadronic medicine of some actions by biological entities beyond our sensory perception; 5) The expected diagnostic and curative values of hadronic medicine.