Haven't got space for conservation

Consider a system with $N$ particles whose coordinates are $\mathbf{r}_i = \{r_i^x,r_i^y,r_i^z\}$, and whose velocities are $\dot{\mathbf{r}}_i$. The energy of the system is described by the kinetic energy $\frac{1}{2}m\sum \dot{\mathbf{r}}^2$ and an effective potential energy term $V\left(\mathbf{r}_1, \ldots, \mathbf{r}_N\right).$

All we know about $V$ is that it depends on the positions only through their differences $\mathbf{r}_1 - \mathbf{r}_2$, i.e. $V(\{\mathbf{r}^i\}, t) = V\left(\mathbf{r}_1-\mathbf{r}_2, \mathbf{r}_1-\mathbf{r}_3, \ldots, t\right).$ As this system evolves in time, which of the following bulk quantities must be conserved?

Assumptions

• All interactions of the system with the outside world are described by $V.$