Baryon number B appears to be a conserved quantity in the Standard Model of particle physics, though there are compelling theoretical reasons to believe it isn't. This thesis describes searches for processes that violate B by two units with the Super-Kamiokande experiment. Two types of searches are performed. One is the simultaneous decay of two bound nucleons to pions (dinucleon decay), encompassing the modes ^16O() → ^14C ^+^+, ^16O() → ^14N ^+^0, and ^16O() → ^14O ^0^0. The second is a search for a neutron transforming into an antineutron, or neutron-antineutron oscillation → n̄.
This thesis uses the full dataset across four Super-Kamiokande detector periods from April 1996 to March 2015, comprising 4972.4 livetime days (307 kiloton-years). Monte Carlo simulations of the signal processes and their background from atmospheric neutrino interactions are used to estimate signal efficiency, expected background, and their associated uncertainties. Both multivariate analyses and simple kinematical cuts are applied in these searches. This is the first search for dinucleon decay to pions in oxygen. The search for → n̄ entails some important updates from a previous search at Super-Kamiokande, mainly increased exposure and an improved model of pion interactions. For all but the single mode ^16O() → ^14O ^0^0, it is found that a boosted decision tree multivariate method gives the best signal-background separation, while for ^16O() → ^14O ^0^0 a set of simple kinematic cuts suffice.
In each mode investigated, no signal excess was observed, and all data are consistent with atmospheric neutrino background. In the absence of evidence for any signal process, lower lifetimes are set at the 90% confidence level. For dinucleon decay, the limits are
_→^+^+ > 7.2 × 10^31 years, _→^+^0 > 1.7 × 10^32 years, and _→^0^0 > 4.0 × 10^32 years. These limits are about two orders of magnitude more stringent than those set by previous searches for dinucleon decay in iron. For → n̄, the limit for bound neutrons is
_bound > 2.4 × 10^32 years, corresponding to a free neutron lifetime _free > 3.8 × 10^8 s. This is comparable with previous results from Super-Kamiokande and other experiments
