This paper will introduce the concept of Architecture Entropy in the context of systems engineering and complex systems. Entropy has been explored and discussed in other domains, drawing an analogy to its origins in physics. In its original context, entropy describes the degree of randomness, or level of chaos, that occurs over time. The purpose of this research is to explore application of the concept of entropy for understanding the vitality of legacy system architectures. The discussion is supported by examples of current architecture challenges that may be attributed to architectural entropy. Specific examples are presented to better understand the applicability of architectural entropy.