The drainage basins of Greece are analyzed in terms of hierarchy and discussed in view of Tsallis Entropy. This concept has been successfully used in a variety of complex systems, where fractality, memory and long-range interactions are dominant. The analysis indicates that the statistical distribution of drainage basins' area in Greece, presents a hierarchical pattern that can be viewed within the frame of non-extensive statistical physics. Our work was based on the analysis of the ASTER GDEM v2 Digital Elevation Model of Greece, which offers a 30 m resolution, creating an accurate drainage basins' database. Analyzing the drainage size (e.g., drainage basin area)-frequency distribution we discuss the connection of the observed power law exponents with the Tsallis entropic parameters, demonstrating the hierarchy observed in drainage areas for the set created for all over Greece and the subsets of drainages in the internal and external Hellenides that are the main tectonic structures in Greece. Furthermore, we discuss in terms of Tsallis entropy, the hierarchical patterns observed when the drainages are classified according to their relief or the Topographic Position Index (TPI). The deviation of distribution from power law for large drainages area is discussed.Appl. Sci. 2020, 10, 248 2 of 18 activity. As a result the complex interaction between earth's surface and tectonic processes plays a key role in geomorphological evolution [7]. Tectonic activity generates complex relief that controls surface processes such as erosion patterns, drainage network development, sedimentary basin growth, and local climate [8][9][10][11][12]. Moreover, erosion, transport and sedimentation induce large mass transfer that changes the dynamical equilibrium of orogenic wedges and trigger mechanical actions [8,13]. The continuous evolution of the aforementioned processes, in a dynamical non-linear feedback indicates a system in a dynamical non-equilibrium stage where long-range interactions and memory effects are dominant.In this context, geomorphologists have studied the evolution of drainages in time and found it to be driven by local conditions due to erosion, natural damming, tectonic motion, as well as volcanic activity [14][15][16]. A drainage basin is an area of land that drains all the streams and rainfall to a common outlet such as the outflow of a reservoir, mouth of a bay, or any point along a stream channel. Drainage basins as conceptual or physical entities are used in water management [17,18], landsliding processes control [19] and flood control [20,21].According to Strahler and Strahler [22], the development of a drainage system (i.e., a stream network and its drainage basin) can be described as follows: Initially, the stream is established on a land surface dominated by landforms of tectonic activity. In a next stage, the channels are deepening due to gradation resulting in steep gorges while the stream tributaries extend into the land carrying out a drainage basin and transforming the landscape into a fluvial landform...