在有效场论中，高阶导数算符的正定性约束源于解析性、因果性和幺正性。我们证明，有效场论中某些算符的正定性约束（例如：单个无质量标量场的八维项、Standard Model Effective Field Theory 的八维 $SU(N)$ 规范玻色子算符，以及 Einstein-Maxwell 理论中的高阶导数算符）由重与轻自由度间的相互作用产生，可由相对熵的非负性推导得出。对于此类有效场论，我们证明在固定电荷和能量极值点处，相互作用会增加热力学熵，这与展现 Weak-Gravity-Conjecture 的黑洞极值性关系密切相关。当涉及轻场高阶导数算符的相互作用修正不占主导地位时，这些论证适用。该熵约束是哈密顿量厄米性的推论，任何违反熵非负性的理论都将不遵循热力学第二定律。
英文摘要：
In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on some operators of the effective field theory, e.g., dimension-eight term of a single massless scalar field, the Standard Model Effective Field Theory dimension-eight $SU(N)$ gauge bosonic operators, and higher-derivative operators in the Einstein-Maxwell theory, generated by interactions between heavy and light degrees of freedom can be derived by the non-negativity of relative entropy. For such effective field theories, we prove that the interactions increase thermodynamic entropy at a fixed charge and an extremal point of energy, which is intimately connected with the extremality relations of black holes exhibiting Weak-Gravity-Conjecture. These arguments are applicable when corrections from the interactions involving higher-derivative operators of light fields are not dominant in the effective field theories. The entropy constraint is a consequence of the Hermiticity of Hamiltonian, and any theory violating the non-negativity of entropy would not respect the second law of thermodynamics.
Gravitational Waves and Matter Constraints in Gravity from Entropy
Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院）；Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院空间科学与天体物理研究所）
