Hot replicas cross barriers easily but sample a distribution you do not care about. Cold replicas sample the right distribution but get trapped. An exchange lets a configuration that a hot replica found walk down the ladder into the cold one, and a stuck cold configuration walk up and escape.

Swaps are accepted or rejected by a Metropolis criterion built from the two potential energies and the two temperatures, which is what keeps each replica's statistics correct. Only neighbouring temperatures are tried, because the energy distributions of distant replicas barely overlap and the swap would almost always be rejected.

Aim for an acceptance rate around 20 to 30 per cent. Much lower and the replicas never mix, so you have paid for many independent simulations. Much higher and your ladder is too dense, so you are paying for replicas that are barely distinguishable.

Sixteen replicas is sixteen times the compute of one run, and mdrun wants them running together with -multidir so the exchanges can happen. Size the machine for the whole ladder, not for one replica, and decide before you start whether the barrier you are trying to cross is worth that bill.