  Non-equilibrium state can exhibit the same macroscopic properties, such as
conductivity or superconductivity, as a static state when they share the
identical average of an observable over a period of time. We investigate the
quench dynamics of a Kitaev chain by introducing two kinds of order parameters
which relate to two channels of pairing, local pair in real space and BCS-like
pair in momentum space. Based on exact solutions, we find that two order
parameters are identical for the ground state, indicating the balance between
two kinds of pairing channels, and can identify the quantum phase diagram.
However, for a non-equilibrium state obtained by the time evolution from
initially prepared vacuum state, the two are different but both can still
clearly identify the phase diagram. In the topologically non-trivial region,
the non-equilibrium states prefer the BCS-like pairing state. Our finding
provides an alternative way to dynamically generate a superconducting state
from a trivial empty state and sheds light on the mechanism of pairing.
