  Heat capacity is an invaluable quantity in condensed matter physics, yet it
has been so far experimentally inaccessible in two-dimensional (2D) van der
Waals (vdW) materials, owing to their ultra-fast thermal relaxation times and
the lack of suitable nano-scale thermometers. Here, we demonstrate a novel
thermal relaxation calorimetry scheme that allows the first measurements of the
electronic heat capacity of graphene Ce. It is enabled by the grouping of a
radio-frequency Johnson noise thermometer, which can measure the electronic
temperature Te with a measurement sensitivity of {\delta}Te ~ 20 mK, and an
ultra-fast photo-mixed optical heater, which can simultaneously modulate Te
with a frequency of up to {\Omega}=0.2 THz. This combination allows record
sensitive and record fast measurements of the electronic heat capacity Ce <
10^(-19) J/K, with an electronic thermal relaxation time {\tau}e < 10^(-13),
representing orders of magnitude improvements as compared to previous
state-of-the-art calorimeters. These features embody a breakthrough in heat
capacity metrology of nano-scale and low-dimensional systems, and provide a new
avenue for the investigation of their thermodynamic quantities.
