A mini-max principle for the system of the drift waves and mesoscale fluctuations (e.g. zonal flows, etc) is studied. For the system of model equations a Lyapunov function is constructed, which takes the minimum when the stationary state is realized. The dynamical evolution describes the access to the state that is realized. The competition between different mesoscale fluctuations is explained. The origins of irreversibility that cause an approach to the stationary state are discussed. A selection rule among fluctuations is derived, and conditions, under which different kinds of mesocale fluctuations coexist, are investigated. An analogy of this minimum principle to the principle of 'minimum Helmholtz free energy' in thermal equilibrium is shown.
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