While reading up about Conway's Game of Life, I often come across the term conservative or non-conservative dynamics. What exactly does these terms mean?
My guess is that a certain quantity (e.g., number of dead cells) always remains the same as the system evolves. Is this what it means? Thank you.
The paper I was looking at is "Phase transitions in a Conservative Game of Life" by Hans J. Herrmann (https://arxiv.org/pdf/2101.07225.pdf)
Some relevant quotes from the paper:
We investigate the dynamics of a conservative version of Conway’s Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway’s rules but only by swapping their positions, irrespective of their mutual distance.
A common feature of these previous studies is that they preserve the nonconservative nature of the dynamical rules. Here, on the other hand, we modify the dynamical rules in order to enforce conservation of the number of cells of both types.
In contrast to the original version of the Game of Life, we assume a conservative, asynchronous and nonlocal dynamics: at each time step, we randomly select an unsatisfied living cell and an unsatisfied dead cell and we switch their states
In other words, a dynamics is conservative if it conserves the number of cells of each type.
