  The above comment http://dx.doi.org/10.1088/0953-8984/22/42/428001 and a
previous letter by the same author reveal a great misunderstanding of what
Eulerian and Lagrangian quantities are, and a confusion between the deformation
of an element of a surface and the creation of a new element of a surface.
Surface thermodynamics is complex because the surface quantities are not
'intuitive' (as surface excesses on some dividing surface) and the
thermodynamic variables of the state of a surface are a priori completely
unknown. This is why we introduced a new concept ('ideal transformation') and
presented detailed proof, leading to the determination of the 'local'
thermodynamic variables of the state of the surface, the exact expression of
the work of deformation of the surface, and the definition of surface stress,
for any deformable body (Olives 2010 J. Phys.: Condens. Matter 22 085005,
arXiv:arXiv:1906.11022). These results are not obvious (despite their
similarity with some expressions in volume thermodynamics). We explicitly write
the Eulerian forms of (i) the relation between the surface grand potential per
unit area, the surface stress and the surface strain, showing its exact
equivalence with the Lagrangian form, and (ii) the variation of the surface
energy due to both the deformation of an element of the surface and the
creation of a new element of the surface.
