Abstract classes serve as templates for concrete classes and play a pivotal role in Java's abstraction mechanisms. Explore the concept of abstract classes and their significance in Java programming. How do abstract classes enable developers to define common behaviors and characteristics shared among multiple subclasses? Delve into the principles of abstraction and inheritance that underpin the design of abstract classes. Additionally, reflect on the relationship between abstract classes and polymorphism. How does the use of abstract classes facilitate the implementation of polymorphic behavior in Java applications, and what are the best practices for utilizing abstract classes effectively? Finally, discuss the limitations and trade$-$offs associated with abstract classes compared to interfaces, and examine scenarios where abstract classes are preferred over interfaces for achieving code reusability and extensibility.