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*dU * = *Mdt = *δ*Q* - dH; M > 0

**Biology** is “the study of those systems that can replace their internal energy” (See explanation of terms and variables).

*pdt + mdt = dh + du = *δ*q**; m * > 0

**Ecology **is “the study of the processes systems use to replace their internal energy” (See explanation of terms and variables).

The Gibbs-Duhem equation governs all biological energy:

*m*̅μ = *m̅**dS* = *dU* + *dH* - Σ_{i} μ_{i}(*dv*_{i} - *dm*_{i})

The Euler equation governs all biological activity:

μ = *dS* = (∂*S*/∂*U*)_{V,Ni} *dU* + (∂*S*/∂*V*)_{U,Ni} *dV* +
Σ_{i} (∂*S*/∂*u*_{i})_{U,V,{Nj≠i}} *du*_{i} + Σ_{i} (∂*S*/∂*v*_{i})_{U,V,{Nj≠i}} *dv*_{i}.

All biological populations are subject to the three constraints of:

(a) constant propagation, ;(b) constant size, ;

(c) constant equivalence, .