Kinetic scheme

In physics, chemistry and related fields, a kinetic scheme is a network of states and connections between them representing a dynamical process.

Usually a kinetic scheme represents a Markovian process, while for non-Markovian processes generalized kinetic schemes are used.

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,

In a Markovian kinetic scheme the connections are constant with respect to time (and any jumping time probability density function for state i is an exponential, with a rate equal the value of all the exiting connections).

When detailed balance exists in a system, the relation

The result represents the fact that any closed loop in a Markovian network in equilibrium does not have a net flow.

can also represent birth and death, meaning that probability is injected (birth) or taken from (death) 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.