Is it possible in lammps to have all atoms interacting no matter in what processor they fall? In other words can lammps handle a system where all atoms interact in a pairwise potential with all the atoms (not just the ones in the neighboring list) coupled with each other with no need anymore of buliding a neighbor list
It is not clear to me f.e in Ewald type potential how an atom will interact with a distinct one that falls in a far processor and his not a ghost of the neighboring one.
I am asking because I am trying to implement an expansion in a polynomial base of a long range ewald yukawa potential which should have all the atoms interact without referring to the kspace.
Any comment or suggestion is highly appreciated.

Is it possible in lammps to have all atoms interacting no matter in what processor they fall? In other words can lammps handle a system where all atoms interact in a pairwise potential with all the atoms (not just the ones in the neighboring list) coupled with each other with no need anymore of buliding a neighbor list

technically yes, practically, it will require extra programming work.
you basically have to turn off neighbor lists and then just collect/broadcast
all atom positions from the "local" atoms across all MPI tasks.
several parts of lammps collect this information, so you can "borrow" the
code from there.

you will run into scaling issues, since your algorithm scales O(N**2),
provided you stick to minimum image coordinates. if you want to use
an arbitrary long cutoff, you have a serious issue.

It is not clear to me f.e in Ewald type potential how an atom will interact with a distinct one that falls in a far processor and his not a ghost of the neighboring one.

ewald sum is a lattice summation "trick". compute
the interactions twice, once in real space and once
in reciprocal space. however to avoid any double counting,
you add a charge cloud around each charge in real space
and subtract it in reciprocal space. that turns both sums
that would normally converging slowly into fast converging
sums. you can lookup the details of how this works in any
MD text book.

I am asking because I am trying to implement an expansion in a polynomial base of a long range ewald yukawa potential which should have all the atoms interact without referring to the kspace.
Any comment or suggestion is highly appreciated.

this sounds strange to me. would would be the benefit?

If your system in non-periodic, just use a long cutoff and you'll
compute N^2 interactions. If your system is periodic, then
what you're asking isn't well defined (you can't compute an
infinite number of pairwise interactions), so a Kspace method
is your only option.