I have two equations from the article "Autopoiesis: a review and a reappraisal" [1] that [attempt to] describe biological systems:
$$ \begin{align} v_\mathrm{gen} &= \frac{d[s]}{dt}\label{eq:1}\tag{1}\\ v_\mathrm{dec} &= -\frac{d[s]}{dt}\label{eq:2}\tag{2}\\ \end{align} $$
When $\eqref{eq:1}=\eqref{eq:2}$, then we have homeostasis.
When $\eqref{eq:1}>\eqref{eq:2}$, then we have growth.
When $\eqref{eq:1}<\eqref{eq:2}$, we have senescense.
What do the square brackets mean around $s$? This seems critically important to the overall claim of the equations because if this leads to a simple related rates problem, then that over-simplifies the definition of life. I would think $s$ would have to be a set of some chemical system or properties that would make the relation between $\eqref{eq:1}$ and $\eqref{eq:2}$ more complicated.
Reference
- Luisi, P. L. Naturwissenschaften 2003, 90 (2), 49–59. DOI: 10.1007/s00114-002-0389-9.
$[\mathrm{S}]$ is chemistry notation for the concentration of $\mathrm{S}$. So they're talking about the rate of change of concentrations of $\mathrm{S}$.
The notation is very sloppy in defining $v_\mathrm{gen}$ and $v_\mathrm{dec}$, though. $v_\mathrm{gen}$ is the rate of change of concentration in some reaction $\mathrm{A \to S}$ and $v_\mathrm{dec}$ is the negative rate of change in some reaction $\mathrm{S \to P}$.
There's a little bit of an explanation in this link about what's going on, on pages 161 and 162.