  Small variations of the entanglement entropy \delta S and the expectation
value of the modular Hamiltonian \delta E are computed holographically for
circular entangling curves in the boundary of AdS(4), using gravitational
perturbations with general boundary conditions in spherical coordinates.
Agreement with the first law of thermodynamics, \delta S = \delta E, requires
that the line element of the entangling curve remains constant. In this
context, we also find a manifestation of electric-magnetic duality for the
entanglement entropy and the corresponding modular Hamiltonian, following from
the holographic energy-momentum/Cotton tensor duality.
