We analyze the generic structure of Einstein tensor projected onto a 2D spacelike surface S defined by a unit timelike and spacelike vectors u and n, respectively, which describe an accelerated observer (see text). Assuming that flow along u defines an approximate Killing vector ξ, we then show that near the corresponding Rindler horizon, the flux ja=Gbaξb along the ingoing null geodesics k, i.e., j•k, has a natural thermodynamic interpretation. Moreover, change in the cross-sectional area of the k congruence yields the required change in area of S under virtual displacements normal to it. The main aim of this paper is to clearly demonstrate how, and why, the content of Einstein equations under such horizon deformations, originally pointed out by Padmanabhan, is essentially different from the result of Jacobson, who employed the so-called Clausius relation in an attempt to derive Einstein equations from such a Clausius relation. More specifically, we show how a very specific geometric term (reminiscent of Hawking's quasilocal expression for energy of spheres) corresponding to change in gravitational energy arises inevitably in the first law: dEG/dλHd2x√σR(2) (see text)-the contribution of this purely geometric term would be missed in attempts to obtain area (and hence entropy) change by integrating the Raychaudhuri equation. © 2011 The American Physical Society.