# Do "minimum image convention" and "nearest image" talks about the same things?

I am a little bit confused by the terminologies of Molecular Dynamics simulation.

Do "minimum image convention" and "nearest image" talks about the same things?

What is their relationship with the "neighbor list"?

Neighbour list is what the name suggests that it is. It is computationally expensive to calculate non-bonded interactions between all pairs of particles in an MD simulations, because a naive brute force approach would be an $$N^2$$ algorithm. So, what is usually done is that you store the id of all particles that are within a specified distance from a given particle in a neighbour list, and calculate the interactions. You then flush this list with a frequency of some multiple times your time step for the simulations.
Computing interactions often requires determining the distances between the particles, $$\Delta {\bf r}_{ij}={\bf r}_{i}-{\bf r}_{j}$$. When periodic boundary conditions are employed, one needs to take into account the fact that the distance between the particles may be shorter when their periodic images are also taken into account.
The minimum image convention is simply an easy way to implement periodicity. Assuming cubic boundary conditions, you would simply compute the minimal distance along every direction. For instance, the minimum image convention along the $$x$$ axis is $$-\frac 1 2 L_x \le (\Delta {\bf r}_{ij})_x < \frac 1 2 L_x$$, which is achieved by adding or substracting $$L_x$$ from $$x$$ component of $$\Delta {\bf r}_{ij}$$ the necessary number of times.
The convention can also be used with non-orthorhombic cells; in that case, you just need to repeat the analysis with the non-orthogonal $${\bf L}_i$$ vectors instead of the individual cartesian components.