Physics of Computational Complexity

A Physics of Computational Complexity is a theoretical framework that interprets computational complexity classes as fundamental physical constraints on information processing in the universe.

• AKA: P vs NP Physics Framework, Informational Universe Hypothesis, LNS Complexity Theory, Natural Systems Complexity Physics.
• Context:
  • It can typically relate P versus NP Question to physical realizability.
  • It can typically constrain Computational Model through thermodynamic limits.
  • It can typically unify Complexity Theory with quantum mechanics.
  • It can typically inform Natural System Modeling through complexity bounds.
  • ...
  • It can often suggest Algorithm Design Principles through physical analogy.
  • It can often provide Complexity Lower Bounds through energy considerations.
  • It can often bridge Computer Science with theoretical physics.
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  • It can range from being a Classical Physics of Computational Complexity to being a Quantum Physics of Computational Complexity, depending on its physics of computational complexity quantum incorporation.
  • It can range from being a Discrete Physics of Computational Complexity to being a Continuous Physics of Computational Complexity, depending on its physics of computational complexity mathematical structure.
  • ...
  • It can integrate with Learnable Natural System for complexity classification.
  • It can connect to Computational Complexity Theory for formal analysis.
  • It can interface with Quantum Computing System for physical implementation.
  • It can communicate with Information Theory for entropy bounds.
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• Example(s):
  • Thermodynamic Complexity Bounds, such as:
    • Landauer's Principle Application for computational energy limits.
    • Maxwell's Demon Analysis for information-energy equivalence.
    • Reversible Computing Theory for energy-efficient computation.
  • Quantum Complexity Frameworks, such as:
    • BQP Physical Interpretation for quantum advantage boundary.
    • Quantum Supremacy Physics for classical intractability.
    • Topological Quantum Computing for error-resistant computation.
  • LNS Complexity Classes, such as:
    • Protein Folding Complexity for biological system tractability.
    • Climate Modeling Complexity for environmental prediction limits.
    • Neural Network Learnability for AI system capability.
  • ...
• Counter-Example(s):
  • Pure Mathematical Complexity, which lacks physical grounding.
  • Engineering Complexity, which lacks fundamental constraints.
  • Algorithmic Complexity, which lacks universal physical laws.
• See: P versus NP Question, Computational Complexity Theory, Learnable Natural System, Quantum Computing, Information Theory, Thermodynamics of Computation, Natural Computation.

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