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 Markovian kinetic scheme

Mathematical description

A kinetic scheme is a network of distinct states, where each pair of states i and j are associated with directional rates, . It is described with a master equation: a first-order differential equation for the probability of a system to occupy each one its states at time t. Written in a matrix form, this states:, where is the matrix of connections .
In a Markovian kinetic scheme the connections are constant with respect to time.
When detailed balance exists in a system, the relation holds for every connected states i and j. The result represents the fact that any closed loop in a Markovian network in equilibrium does not have a net flow.
Matrix can also represent birth and death, meaning that probability is injected or taken from the system, where then, the process is not in equilibrium. These terms are different than a birth-death process, where there is simply a linear kinetic scheme.

Specific Markovian kinetic schemes

An example for such a process is a reduced dimensions form.