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There are three basic processes that determine hopping transport: (a) hoppingbetween normally empty sites (i.e. having exponentially small occupationnumbers at equilibrium); (b) hopping between normally occupied sites, and (c)transitions between normally occupied and unoccupied sites. In conventionaltheories all these processes are considered Markovian and the correlations ofoccupation numbers of different sites are believed to be small(i.e. notexponential in temperature). We show that, contrary to this belief, memoryeffects suppress the processes of type (c), and manifest themselves in asubleading {\em exponential} temperature dependence of the variable rangehopping conductivity. This temperature dependence originates from the propertythat sites of type (a) and (b) form two independent resistor networks that areweakly coupled to each other by processes of type (c). This leads to atwo-color percolation problem which we solve in the critical region.

Memory effects, two color percolation, and the temperature dependence of Mott's variable range hopping