A new simplified model is discussed that is able to yield the previously reported isothermal Maxwell demon property, i.e., active behavior of the thermodynamic bath (reservoir) upon particle transfer. In contrast to previous models, the present one works with extended modes of the bath. It is shown that and how the cooperation self-organization effects induced in the bath by the transferred particle can appreciably modify detailed balance important for, e.g., electron-transfer reactions. Ensuing effects include single-particle rectification (prevailingly unidirectional transfer preferring thus one direction of the reaction), prevailingly uphill particle transfer at the cost of energy of a single and typically nonequilibrium infinite bath, and induced particle self-organization. The model provides a basis for treating dynamic self-organization in open quantum systems.