Table 1  List of symbols
SymbolDescription
N, u, sPopulation size, mutation rate, and mutation effect
Embedded ImageNumber of individuals in class k at time t, steady-state value
λ = u/s, τ = tsRescaled mutation rate and time
Embedded ImagePopulation frequency in class k at time τ, steady-state value
zτ, Embedded ImageAbbreviation for x0(τ) and Embedded Image
Embedded ImageMean fitness: Embedded Image
Embedded Image, Embedded ImageDeviations from steady state: Embedded Image, Embedded Image
Sλ({zρ})Path integral action depending on the path {zρ} with 0 ≤ ρτ.
Embedded Image, Embedded ImageExtremal action and the associated path depending on the endpoints zτ, z0
Embedded ImageLong time limit of Embedded Image with z = zτ
Pτ(zτ|z0)Propagator from z0 to zτ in time τ
P(z)Steady-state distribution of z
γRate of the ratchet in units of s
σ2Variance of x0 depending on Ns and λ
ζ2Rescaled variance of x0 depending on λ only: ζ2 = Nseλσ2
Embedded Image, Embedded Imagekth component of right and left eigenvectors with eigenvalue −i
ai(τ)Projection of δxk on Embedded Image
αParameter of the effective potential confining x0 (traditionally α = 0.5−0.6)