Kinetic scheme

In physics, chemistry and related fields, a kinetic scheme is a network of states and connections between them representing the scheme of a dynamical process. Usually a kinetic scheme represents a Markovian process, while for non-Markovian processes generalized kinetic schemes are used. Figure 1 shows an illustration of a kinetic scheme.

A kinetic scheme is a network (a directed graph) of distinct states (although repetition of states may occur and this depends on the system), where each pair of states i and j are associated with directional rates, ${\displaystyle A_{ij}}$ (and ${\displaystyle A_{ji}}$). It is described with a master equation: a first-order differential equation for the probability ${\displaystyle {\vec {P}}}$ of a system to occupy each one its states at time t (element i represents state i). Written in a matrix form, this states: ${\displaystyle {\frac {d{\vec {P}}}{dt}}=\mathbf {A} {\vec {P}}}$, where ${\displaystyle \mathbf {A} }$ is the matrix of connections (rates) ${\displaystyle A_{ij}}$.

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