  We derive the notions of BV unital infinitesimal bialgebra and BV Frobenius
algebra from the topology of suitable compactifications of moduli spaces of
decorated genus 0 curves. We construct these structures respectively on reduced
symplectic homology and Rabinowitz Floer homology. As an application, we
construct these structures in nonequivariant string topology. We also show how
the Lie bialgebra structure in equivariant string topology, and more generally
on $S^1$-equivariant symplectic homology, is obtained as a formal consequence.
