Our conventions for the infinitesimal charges associated with symmetries is as follows: the energy is δℳ = δ𝒬 ∂t, the angular momentum is δ𝒥 = δ𝒬 − ∂ϕ and the electric charge is δ𝒬 = δ𝒬 e −∂χ. In other words, the electric charge is associated with the gauge parameter Λ = − 1. The first law then reads T δ𝒮 = δℳ − Ω δ𝒥 − Φ δ𝒬 H J e e.