  The weak gravity conjecture suggests that, in a self-consistent theory of
quantum gravity, the strength of gravity is bounded from above by the strengths
of the various gauge forces in the theory. In particular, this intriguing
conjecture asserts that in a theory describing a U(1) gauge field coupled
consistently to gravity, there must exist a particle whose proper mass is
bounded (in Planck units) by its charge: $m/m_{\text{P}}<q$. This beautiful and
remarkably compact conjecture has attracted the attention of physicists and
mathematicians over the last decade. It should be emphasized, however, that
despite the fact that there are numerous examples from field theory and string
theory that support the conjecture, we still lack a general proof of its
validity. In the present Letter we prove that the weak gravity conjecture (and,
in particular, the mass-charge upper bound $m/m_{\text{P}}<q$) can be inferred
directly from Bekenstein's generalized second law of thermodynamics, a law
which is widely believed to reflect a fundamental aspect of the elusive theory
of quantum gravity.
