Provide a theoretical analysis of the P versus NP problem, explaining its significance in computer science and mathematics. Define complexity classes P, NP, NP-complete, and NP-hard, explaining the relationships between them. Discuss the theoretical implications of possible resolutions to the P versus NP problem, including its impact on cryptography, optimization, and our understanding of computation. Explore connections between computational complexity and other theoretical frameworks, including information theory, quantum computing, and physics.