Particle color distance to empty in Eeevee? Is there a way to do this with material nodes only?

I can find a particle info node:

https://docs.blender.org/manual/en/latest/render/shader_nodes/input/particle_info.html

But the object info node doesn't have an input... the texture coordinate node does have an input for a different object, but then I can't find the distance node:

https://docs.blender.org/manual/en/latest/editors/texture_node/types/converter/distance.html
The distance node is part of the (kinda-deprecated) texture node editor, which is different from the shader node editor. To get the distance between two locations, use a vector Math node set to Distance.



Result :



Note : The shader should go on the particle object, not on the instancer.