明细余额=综合余额+周期余额。反应网络和马尔可夫链的图论证明
Detailed balance = complex balance + cycle balance. A graph-theoretic proof for reaction networks and Markov chains
摘要：
进一步阐明了可逆化学反应网络的详细平衡态与复杂平衡态之间的关系。我们的结果适用于任意动力学和边界平衡。详细平衡、复杂平衡、“形式平衡”和“循环平衡”的新概念都是根据基础图来定义的。这一事实允许初等图论（非代数）证明以前的结果（详细平衡=复平衡+形式平衡），我们的主要结果（详细平衡=复平衡+循环平衡），以及相应的结果在设置连续时间马尔可夫链。
英文摘要：
We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, "formal balance", and the new notion of "cycle balance" are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic (non-algebraic) proofs of a previous result (detailed balance = complex balance + formal balance), our main result (detailed balance = complex balance + cycle balance), and a corresponding result in the setting of continuous-time Markov chains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
