Problem Complexity Research from Energy Perspective

Computational complexity is a particularly important objective. The idea of Landauer principle was extended through mapping three classic problems (sorting、 ordered searching and max of N unordered numbers) into Maxwell demon thought experiment in this paper. The problems’ complexity is defined on the entropy basis and the minimum energy required to solve them are rigorous deduced from the perspective of energy (entropy) and the second law of thermodynamics. Then the theoretical energy consumed by real program and basic operators of classical computer are both analyzed, the time complexity lower bounds of three problems’ all possible algorithms are derived in this way. The lower bound is also deduced for the two n n × matrix multiplication problem. In the end, the reason why reversible computation is impossible and the possibility of super-linear energy consumption capacity which may be the power behind quantum computation are discussed, a conjecture is proposed which may prove NP!=P. The study will bring fresh and profound understanding of computation complexity. Key word: Landauer principle, Entropy, Second law of thermodynamics, reversible computation, NP-Complete problem, Quantum computation PACS number: 89.70.-a