  There is an interesting relation between the quantum periods on a certain
limit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and a TBA
(Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM
(Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parameter
generalization of the relation. Furthermore, we derive the differential
operators for quantum periods and the TBA-like equation in various limits of
the generalized relation.
