  Heat generated as a result of the breakdown of an adiabatic process is one of
the central concepts of thermodynamics. In isolated systems, the heat can be
defined as an energy increase due to transitions between distinct energy
levels. Across a second-order quantum phase transition (QPT), the heat is
predicted theoretically to exhibit a power-law scaling, but it is a significant
challenge for an experimental observation. In addition, it remains elusive
whether a power-law scaling of heat can exist for a first-order QPT. Here we
experimentally observe a power-law scaling of heat in a spinor condensate when
a system is linearly driven from a polar phase to an antiferromagnetic phase
across a first-order QPT. We experimentally evaluate the heat generated during
two non-equilibrium processes by probing the atom number on a hyperfine energy
level. The experimentally measured scaling exponents agree well with our
numerical simulation results. Our work therefore opens a new avenue to
experimentally and theoretically exploring the properties of heat in
non-equilibrium dynamics.
