Large deviations and dynamical phase transitions in stochastic chemical networks
Large deviations and dynamical phase transitions in stochastic chemical networks
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DOI：
10.1063/1.5111110
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发表时间：
2019-08-14
影响因子：
4.4
通讯作者：
Esposito, Massimiliano
中科院分区：
文献类型：
--
作者：
Lazarescu, Alexandre;Cossetto, Tommaso;Esposito, Massimiliano
化学反应网络是有限状态空间上线性马尔可夫跳变过程的自然非线性推广。在本文中，我们分析了这种模型的动力学大偏差，从他们的微观版本，化学主方程。通过采取大体积的限制，我们表明，这些系统可以描述的路径积分形式主义的浓度和化学通量的拉格朗日函数。该拉格朗日量与哈密顿量是对偶的，哈密顿量的轨迹对应于给定其边界条件的系统的最可能的演化。对于一个偏向于时间平均浓度和电流的系统，也可以这样做，得到一个偏向的哈密顿量，其轨迹是以这些观测值为条件的最佳路径。适当的边界条件是混合的，这样，在很长的时间限制，这些轨迹收敛到定义明确的吸引子。然后，我们能够确定的最大值的哈密顿量接管这些吸引子与我们的观测量的标度累积量生成函数，提供了一个非线性等效的著名的Donsker-Varadhan公式的跳跃过程。在此基础上，我们证明了确定性多稳态的化学反应网络在零偏置附近一般发生一阶动力学相变。我们说明了这一事实，通过一个简单的muscle模型称为Schlogl模型，以及它的多稳态和不稳定的推广，我们做了一些令人惊讶的观察确定性不动点的稳定性和大容量极限的遍历性的突破。由AIP Publishing授权出版。
Chemical reaction networks offer a natural nonlinear generalization of linear Markov jump processes on a finite state-space. In this paper, we analyze the dynamical large deviations of such models, starting from their microscopic version, the chemical master equation. By taking a large-volume limit, we show that those systems can be described by a path integral formalism over a Lagrangian functional of concentrations and chemical fluxes. This Lagrangian is dual to a Hamiltonian, whose trajectories correspond to the most likely evolution of the system given its boundary conditions. The same can be done for a system biased on time-averaged concentrations and currents, yielding a biased Hamiltonian whose trajectories are optimal paths conditioned on those observables. The appropriate boundary conditions turn out to be mixed so that, in the long time limit, those trajectories converge to well-defined attractors. We are then able to identify the largest value that the Hamiltonian takes over those attractors with the scaled cumulant generating function of our observables, providing a nonlinear equivalent to the well-known Donsker-Varadhan formula for jump processes. On that basis, we prove that chemical reaction networks that are deterministically multistable generically undergo first-order dynamical phase transitions in the vicinity of zero bias. We illustrate that fact through a simple bistable model called the Schlogl model, as well as multistable and unstable generalizations of it, and we make a few surprising observations regarding the stability of deterministic fixed points and the breaking of ergodicity in the large-volume limit. Published under license by AIP Publishing.