  In strongly interacting electron systems with low density and at low
temperature the thermodynamic density of states is negative. It creates
difficulties with understanding of the Einstein relation between conductivity
and diffusion coefficient. Using the expression for electrochemical potential
that takes into account the long range part of the Coulomb interaction it is
shown that at negative density of states Einstein relation gives a negative
sign of the diffusion coefficient D, but under this condition there is no
thermodynamic limitation on the sign of D. It happens because the unipolar
relaxation of inhomogeneous electron density is not described by the diffusion
equation. The relaxation goes much faster due to electric forces caused by
electron density and by neutralizing background. Diffusion coefficient is
irrelevant in this case and it is not necessarily positive because process of
diffusion does not contribute to the positive production of entropy. In the
case of bipolar diffusion negative D results in a global absolute instability
that leads to formation of neutral excitons. Graphene is considered as an
example of a system, where the density relaxation is expected to be due to
electric force rather than diffusion. It may also have a negative density of
states.
