# Haven't got space for conservation

Consider a system of $$N$$ particles whose coordinates are $$\{r_i\}$$, and whose velocities are $$\{\dot{r}_i\}$$. Each pair of particles $$\left(i, j\right)$$ interacts through a potential $$V_{ij}\left(r_i, r_j\right)$$ which depends on the coordinates $$\left(r_i, r_j\right)$$ only through their difference, i.e. $V_{ij}\left(r_i, r_j, t\right) = V_{ij}\left(r_i-r_j, t\right)$ As the system evolves in time, which of the following bulk quantities must be conserved?

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