  A mechanism of the self-organization in an unbounded two-dimensional (2D)
point vortex system is discussed. A kinetic equation for the system with
positive and negative vortices is derived using the Klimontovich formalism.
Similar to the Fokker-Planck collision term, the obtained collision term
consists of a diffusion term and a drift term. It is revealed that the
mechanism for the self-organization in the 2D point vortex system at negative
absolute temperature is mainly provided by the drift term. Positive and
negative vortices are driven toward opposite directions respectively by the
drift term. As a result, well-known, two isolated clumps with positive and
negative vortices, respectively, are formed as an equilibrium distribution.
Regardless of the number of species of the vortices, either single- or
double-sign, it is found that the collision term has following physically good
properties: (i) When the system reaches a quasi-stationary state near the
thermal equilibrium state with negative absolute temperature, the sign of $d
\omega / d \psi$ is expected to be positive, where $\omega$ is the vorticity
and $\psi$ is the stream function. In this case, the diffusion term decreases
the mean field energy, while the drift term increases it. As a whole, the total
mean field energy is conserved. (ii) Similarly, the diffusion term increases
the Boltzmann entropy, while the drift term decreases it. As a whole, the total
entropy production rate is positive or zero ($H$ theorem), which ensures that
the system relaxes to the global thermal equilibrium state characterized by the
zero entropy production.
