Recent developments in nonequilibrium statistical mechanics suggest that the history of entropy production in a system determines the relative likelihood of competing processes. This presents the possibility of interpreting and predicting the self-organization of complex active systems, but existing theories rely on quantities that are challenging to obtain. Here, we address this issue for a general class of Markovian systems in which two types of self-replicating molecular assemblies (self-replicators) compete for a pool of limiting resource molecules within a nonequilibrium steady state. We derive exact relations that show that the relative fitness of these species depends on a path function, ψ, which is a sum of the entropy production and a relative-entropy term. In the limit of infinite path length, ψ reduces to the entropy production. We demonstrate use of the theory by numerically studying two models inspired by biological systems, including a simplified model of a competition between strains of the yeast prion Sup35 in the presence of driven disaggregation by the ATPase Hsp104.
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机译：非平衡统计力学的最新发展表明，系统中熵产生的历史决定了竞争过程的相对可能性。这为解释和预测复杂活动系统的自组织提供了可能性，但现有理论依赖于难以获得的数量。在这里，我们针对一类通用的马尔可夫系统解决了这个问题，其中两种类型的自我复制分子组装体（自我复制器）在非平衡稳态内竞争限制资源分子池。我们推导出精确的关系，表明这些物种的相对适应度取决于路径函数 ψ，它是熵产生和相对熵项的总和。在无限路径长度的限制下，ψ 减少为熵产生。我们通过数值研究受生物系统启发的两个模型来证明该理论的使用，包括在 ATP 酶 Hsp104 驱动解聚存在下酵母朊病毒 Sup35 菌株之间竞争的简化模型。
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