Since the old time of Boltzmann, relationships between entropy and life have been argued until
recently and may be in future. The life span of individual organisms, successional developments of
ecological systems, and the evolution of living systems are shown to be expressed by “Max-Min
Entropy Production Principle” (MMEP)”: entropy production increases with time in the early stage
(birth-growth), and decreases with time in later stage (senescence-death). Thus, Entropy Principle for
the time course of the biological evolution is completely established: the “Biological Thermodynamics”
is completed in this article. Entropy in the universe increases from Big Bang to recently, and
“Maximum Entropy Principle” holds, when proton decay and black hole evaporation are observed, but
not yet now. The validity of the assertion of Clausius: “The entropy tends to a maximum”, and the
validity of the Second Law of Thermodynamics in the universe have not been established until quite
recently (2017); they depend on the observations of proton decay and evaporation of black hole, and
are left for future studies. In the case that protons do not decay and black holes do not evaporate, the
Second Law of Thermodynamics cannot also be proved to be correct in the universe.
Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu City, 432-8561, Japan.
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