 Dimensional analysis and similarity arguments based on dimensionless groups have been used since 1914 to analyze systems in various fields such as science and engineering. These groups are typically divided into three categories, geometric similarity, kinematic similarity, and dynamic similarity. A fourth category, entropic similarity, has recently been proposed, which is based on ratios of entropy production terms, entropy flow rates, or information flow rates. This study demonstrates how many traditional groups, including the Reynolds number, can be recovered using entropic similarity with a different interpretation, while many new groups can also be identified. The analyses significantly expand the scope of dimensional analysis and similarity arguments for the resolution of new and existing problems in science and engineering. This article was authored by Robert K. Niven.