We consider an open system in contact with a reservoir, where particles as well as energies can be exchanged between them, and present a description of the dynamics in terms of mixed (pseudo)spin and state variables. Specifically, a master equation is constructed out of the exchange rates for particles and for energies, which allows us to probe the system in the grand canonical description. In particular, employing the state resummation analysis, we obtain coupled time evolution equations for the probability distributions of the system as well as the environment. This is exemplified by a standard growth model, where the steady-state density function exhibits power-law behavior with the exponent depending on the microscopic parameters of the rate equations.

我们考虑了一个与储层接触的开放系统，在该系统中可以在它们之间交换粒子以及能量，并以混合（伪）自旋和状态变量的形式描述了动力学。具体来说，是根据粒子和能量的交换率构建的主方程，这使我们可以在典范描述中探讨该系统。特别是，使用状态恢复分析，我们获得了系统和环境的概率分布的耦合时间演化方程。这可以通过标准增长模型来说明，其中稳态密度函数显示幂律行为，并且幂率行为取决于速率方程的微观参数。