The abundance of digital text has led to extensive research on topic models that reason about documents using latent representations. Since for many online or streaming textual sources such as news outlets, the number, and nature of topics change over time, there have been several efforts that attempt to address such situations using dynamic versions of topic models. Unfortunately, existing approaches encounter more complex inferencing when their model parameters are varied over time, resulting in high computation complexity and performance degradation. This paper introduces the DM-DTM, a dual Markov chain dynamic topic model, for characterizing a corpus that evolves over time. This model uses a gamma Markov chain and a Dirichlet Markov chain to allow the topic popularities and word-topic assignments, respectively, to vary smoothly over time. Novel applications of the NegativeBinomial augmentation trick result in simple, efficient, closed-form updates of all the required conditional posteriors, resulting in far lower computational requirements as well as less sensitivity to initial conditions, as compared to existing approaches. Moreover, via a gamma process prior, the number of desired topics is inferred directly from the data rather than being pre-specified and can vary as the data changes. Empirical comparisons using multiple realworld corpora demonstrate a clear superiority of DM-DTM over strong baselines for both static and dynamic topic models.