  The connection between the bulk and the boundary first law of thermodynamics
in adS space has been discussed in generic higher derivative gravity. String
theory corrections to the supergravity render higher derivative terms in the
bulk action, proportional to different powers of string theory parameter
$\alpha'$. A variation in the cosmological constant induces a variation in the
't Hooft coupling in the boundary theory. We show that in order to match the
bulk first law and Smarr relation with the boundary side one needs to include
the variation of $\alpha'$ in the bulk thermodynamics as a book keeping device.
Accordingly, the boundary first law and Euler relation are modified with the
inclusion of two central charges ($a$, $c$) and/or other chemical potentials as
thermodynamic variables. We consider four and six derivative terms as well as
the $\text{Weyl}^4$ terms (in type IIB) in bulk in support of our generic
result.
