  In the second part of this two-part paper, we extend the study of dynamic
caching via state transition field (STF) to the case of time-varying content
popularity. The objective of this part is to investigate the impact of
time-varying content popularity on the STF and how such impact accumulates to
affect the performance of a replacement scheme. Unlike the case in the first
part, the STF is no longer static over time, and we introduce instantaneous STF
to model it. Moreover, we demonstrate that many metrics, such as instantaneous
state caching probability and average cache hit probability over an arbitrary
sequence of requests, can be found using the instantaneous STF. As a steady
state may not exist under time-varying content popularity, we characterize the
performance of replacement schemes based on how the instantaneous STF of a
replacement scheme after a content request impacts on its cache hit probability
at the next request. From this characterization, insights regarding the
relations between the pattern of change in the content popularity, the
knowledge of content popularity exploited by the replacement schemes, and the
effectiveness of these schemes under time-varying popularity are revealed. In
the simulations, different patterns of time-varying popularity, including the
shot noise model, are experimented. The effectiveness of example replacement
schemes under time-varying popularity is demonstrated, and the numerical
results support the observations from the analytic results.
