Lets define $P$ a physics over a set $X=\{particles,waves,...\}$ as the the endowement of the set with the relations $E:X \rightarrow X \times X$, where $E$ is the associated energy equilibrium $K:X \rightarrow X \times X$ where $K$ is the transfer of energy relation over time, we would say that $x,y \in X$ are $K$ related if they're exchanging energy.
>Theorem 1
$E$ is an equivalence relationship.

>Proof
Let $x,y,z \in X$

i) $xEx$
We know that $x=x /implies E(x)=E(x)$
ii) $xEy /implies yEx$
We also know that if two elements of $X$ are such that $E(x)=E(y)$ then $E(y)=E(x)$
iii) $xEy$ and $yEz /implies xEz$
It follows from ii) that if the assumption is true then $E(x)=E(z)$

>Theorem
$K$ is also an equivalence relationship.

>Proof
Let $x,y,z \in X$

i) $xKx$
We know that $E(x)=E(x)$ this means that there exists an energy transfer of $x$ of $0$ with itself, so $x$ indeed $K$-related with itself.
ii)$xKy /implies yKx$
We know this holds since $K(x,y)= W \implies K(y,x)=-W$
iii) $xKy$ and $yKz /implies xKz$
We can prove this using ii)

Is this approach right or is it missing something altogether?