The Republic of Neuchâtel is a decision available to 
Switzerland.
It requires that Switzerland owns the province Neuchâtel in West Switzerland and that 
Prussia has a core on said province (which it does at the start of the game). On top of that Switzerland have researched Romanticism and have a prestige score of at least 1. Switzerland starts the game with more than 1 prestige.
It gives 5 prestige, and changes relations with Prussia by 20 and removes the Prussian Core on Neuchâtel. If 
North German Federation or 
Germany is formed by Prussia, and they then have a core on the province, they will lose the core as well. The relation improvement will however not apply to NGF or Germany.