The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information theory, thermodynamics, and computational complexity, offering a comprehensive landscape of interdisciplinary study. We focus on entropy, a concept traditionally linked with uncertainty and disorder, and reinterpret it to assess the complexity of computational problems. Our research presents a structured framework for establishing entropy profiles within computational tasks, enabling a clear distinction between P and NP-classified problems. This framework quantifies the 'information cost' associated with these problem categories, highlighting their intrinsic computational complexity. We introduce Entropy-Driven Annealing (EDA) as a new method to decipher the energy landscapes of computational problems, focusing on the unique characteristics of NP problems. This method proposes a differential thermodynamic profile for NP problems in contrast to P problems and explores potential thermodynamic routes for finding polynomial-time solutions to NP challenges. Our introduction of Entropy-Driven Annealing (EDA) and its application to complex computational problems like the Boolean satisfiability problem (SAT) and protein-DNA complexes suggests a potential pathway toward unraveling the intricacies of the P vs. NP problem.

翻译：P 与 NP 问题作为计算理论的核心难题，尽管已有大量基于数学逻辑和算法理论的研究，但其最终解决仍悬而未决。本文采用新颖的研究路径，整合信息论、热力学与计算复杂性理论，构建了跨学科研究的综合图景。我们聚焦于通常与不确定性和无序性相关的熵概念，对其进行重新诠释以评估计算问题的复杂性。研究提出了一套结构化框架，用于建立计算任务中的熵分布，从而清晰区分 P 类问题与 NP 类问题。该框架量化了这两类问题相关的“信息成本”，揭示了其内在的计算复杂性。我们引入熵驱动退火（EDA）作为一种新方法，用于解析计算问题的能量景观，重点关注 NP 问题的独特特征。该方法提出了 NP 问题相较于 P 问题的差异化热力学特征，并探索了为 NP 挑战寻找多项式时间解的热力学潜在路径。通过将熵驱动退火（EDA）应用于布尔可满足性问题（SAT）和蛋白质-DNA 复合体等复杂计算问题，本研究为揭示 P 与 NP 问题的奥秘开辟了潜在路径。