The evolution of these sparsely coupled states can be expressed as a Langevin or stochastic differential equation; namely, a high dimensional, nonlinear, state-dependent flow plus independent random (Wiener) fluctuations, , with a variance of 2Γ
1
Evolution
states
flow
Stochastic
The flow of Equation 1 can be expressed using the Helmholtz decomposition (expressing the flow as a mixture of a dissipative, gradient flow and a conservative, solenoidal flow)
2
the history or path of a time varying state
the paths of a state-dependent flow are determined by state-dependent flow
Parameters of the state-dependent flow
Initial states of parameters of the state-dependent flow
Partition of states comprising the external, sensory, active and internal states of a phenotype
External State
Active States
Internal State
Sense State
phenotype
Partition
Sensory and active states constitute blanket states
Sense State
Active States
Blanket State
phenotypic states comprise internal and blanket states
phenotype
Internal State
Blanket State
The autonomous states of a phenotype are not influenced by external states:
State
phenotype
External State
independent random (Wiener) fluctuations
Variance of independent random (Wiener) fluctuations is 2Γ.
gradient flow (depends upon the amplitude of random fluctuations)
solenoidal flow (circulates on the isocontours of potential function called self-information)
the nonequilibrium steady-state density (NESS density)
Figure 1: schematic (i.e., influence diagram) illustrating the sparse coupling among states that constitute a particular partition at two scales