Question

How can I define mathematically a system's property?

Answer 1

I don't know... I suppose in classical mechanics you can define a system in terms of action, i.e., the evolution of a system

\[\S\left [ \textbf{q}\left ( t \right ) \right ]=\int\limits L\left [ \textbf{q},\dot{\textbf{q}},t \right ]dt\]

Or the quantum state of a system

\[\left \{ n,l,m_{l},m_{s} \right \}\]

Not sure how else to define "property" in terms of math.