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 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问题的解决是计算理论的基石，尽管通过数学逻辑和算法理论进行了广泛探索，其答案仍未明确。本文采用一种新颖的方法，融合信息论、热力学和计算复杂性，呈现出跨学科研究的全景图。我们聚焦于熵这一传统上与不确定性和无序相关的概念，并重新诠释它以评估计算问题的复杂性。我们的研究提出了一个结构化框架，用于在计算任务中建立熵轮廓，从而能够清晰区分P类和NP类问题。该框架量化了与这些问题类别相关的“信息成本”，凸显了它们固有的计算复杂性。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图景，重点关注NP问题的独特特征。该方法提出了与P问题相比，NP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潜在热力学路径。通过引入EDA并将其应用于布尔可满足性问题（SAT）和蛋白质-DNA复合物等复杂计算问题，我们揭示了破解P与NP问题复杂性的潜在途径。