One of the worst aspects of Civ5 is that you cannot randomly declare war on other civs, you're bound by the game mechanics, so if you're negotiated peace for X many turns through peace treaties then you cannot do any actions which initiate war, that includes moving inside their territory (unless you have an open bordered agreement) or attacking their units.
Remember that peace treaties can be negotiated between you and other civs through the trading menu, so they might offer up peace treaty as part of some larger deal that involves trading money and other goods.
Are peace treaties inherented from civs working together? I'm not sure...it's plausible that if you're at peace with someone you might inherent their peace treaties, a more advanced civ player can probably confirm that I'm never sure because I always ignore diplomacy and just stop other civs