Process mining is concerned with extracting knowledge about business processes based on digital traces left during their execution. Most existing process mining methods are focused on stable processes. However, processes tend to change over time in response to changing regulations or market conditions but also due to internal dynamics. Concept drift is a phenomenon in process mining when a process changes during the timeframe when it is analyzed. Following the change in how a process is executed, process complexity also changes over time. Despite this apparent connection, the relationship between these concepts have not been explicitly studied. In this paper, some theoretical considerations on how concept drift can be reflected in process complexity are presented. These considerations are then evaluated using artificial and real-life event logs. The results support the considerations and invite a multitude of questions for future research.