Generalized second Einstein relation is obtained from a Fokker–Planck equation for a wide class of space-dependent coefficients. The relation is investigated for population growth models.
In this paper, the vulnerability of the Vadai, Mingesz and Gingl (VMG)- Kirchhoff-Law–Johnson-Noise (KLJN) Key Exchanger (Nature, Science Report 5 (2015) 13653) against two active attacks is demonstrated. The security vulnerability arises from the fact that the effective driving impedances are different between the HL and LH cases for the VMG-KLJN scheme; whereas for the ideal KLJN scheme, they are the same. Two defense schemes are shown against these attacks but each of them can protect against only one of the attack types; but not against the two attacks simultaneously. The theoretical results are confirmed by computer simulations.

