  In this work, we explore the statistical physics of colloidal particles that
interact with electrolytes via ion-specific interactions. Firstly we study
particles interact weakly with electrolyte using linear response theory. We
find that the mean potential around a particle is linearly determined by the
{\em effective charge distribution} of the particle, which depends both on the
bare charge distribution and on ion-specific interactions. We also discuss the
effective interaction between two such particles and show that, in far field
regime, it is bilinear in the effective charge distributions of two particles.
We subsequently generalize the above results to the more complicated case where
particles interact strongly with the electrolyte. Our results indicate that in
order to understand the statistical physics of non-dilute electrolytes, both
ion-specific interactions and ionic correlations have to be addressed in a
single unified and consistent framework.
