Abstract
The equilibrium composition of neutron star matter is achieved through weak interactions (direct and inverse beta decays), which proceed on relatively long time scales. If the density of a matter element is perturbed, it will relax to the new chemical equilibrium through non-equilibrium reactions, which produce entropy that is partly released through neutrino emission, while a similar fraction heats the matter and is eventually radiated as thermal photons. We examined two possible causes of such density perturbations: 1) the reduction in centrifugal force caused by spin-down (particularly in millisecond pulsars), leading to rotochemical heating, and 2) a hypothetical time-variation of the gravitational constant G, as predicted by some theories of gravity and current cosmological models (gravitochemical heating). If only slow weak interactions are allowed in the neutron star (modified Urca reactions, with or without Cooper pairing), rotochemical heating can account for the observed ultraviolet emission from the closest millisecond pulsar, PSR J0437-4715, which also provides a constraint on |dG/dt| of the same order as the best available in the literature.