The three constraints

CONSTRAINT 1: The constraint of constant propagation

P > 0 = ∫ T0dP

P is an extensive variable and is the population's “Wallace pressure”—its total energy output in joules per second.

Explanation

CONSTRAINT 2: The constraint of constant size

R > 0 = ∫ T0dR

R is an intensive variable and is the population's average energy output expressed in “darwins” or joules per “biomole”.

Explanation

CONSTRAINT 3: The constraint of constant equivalence

W > 0 = ∫ T0dW

W is an intensive variable and is the population's work rate or its dynamical specific energy, expressed as watts per kilogramme.

Explanation

The Euler equation for biology

μ = dS = (∂S/∂U)V,Ni dU + (∂S/∂V)U,Ni dV + Σi (∂S/∂ui)U,V,{Nj≠i} dui + Σi (∂S/∂vi)U,V,{Nj≠i} dvi

The Gibbs-Duhem equation for biology

m̅μ = m̅dS = dU + dH - Σi μi(dvi - dmi)

Biology is “the study of those thermodynamic systems that can replace their internal energy”.

dU = Mdt = δQ - dH

Ecology is “the study of the exact processes by which a thermodynamic system replaces its internal energy”.

pdt + mdt = dh + du

 

G  O    T  O    E  Q  U  A  T  I  O  N  S

The four laws of biology

brassica rapa experiment

LAW 1: The law of existence
n >= 1; δW = (δQ - dU) > 0; m → ∞; m̅ > 0

LAW 2: The law of equivalence
(δW1 = δW2) ∧ (δW2 = δW3) ⇒ (δW1 = δW3)

LAW 3: The law of diversity
A ⇒ 0; F ⇒ M

LAW 4: The law of reproduction
dA/dt > 0; dm̅/dt < 0; m̅ > 0; dn/dt >= 0

The four maxims of ecology

brassica rapa experiment

MAXIM 1: The maxim of dissipation
[Darwin's theory of competition]
∫dm < 0; ∇• M → 0; M = nm̅

MAXIM 2: The maxim of number
∇• H = δW = Pdt = nh̅

MAXIM 3: The maxim of succession
[Darwin's theory of evolution]
∇ x M = ∂m̅/∂t - ∂n/∂t

MAXIM 4: The maxim of apportionment
∇ x H = ∂m̅/∂t - ∂n/∂t - ∂V/∂t