  Many quantum information theoretic quantities are similar to and/or inspired
by thermodynamic quantities, with entanglement entropy being a well-known
example. In this paper, we study a less well-known example, capacity of
entanglement, which is the quantum information theoretic counterpart of heat
capacity. It can be defined as the second cumulant of the entanglement spectrum
and can be loosely thought of as the variance in the entanglement entropy. We
review the definition of capacity of entanglement and its relation to various
other quantities such as fidelity susceptibility and Fisher information.
  We then calculate the capacity of entanglement for various quantum systems,
conformal and non-conformal quantum field theories in various dimensions, and
examine their holographic gravity duals. Resembling the relation between
response coefficients and order parameter fluctuations in Landau-Ginzburg
theories, the capacity of entanglement in field theory is related to integrated
gravity fluctuations in the bulk. We address the question of measurability, in
the context of proposals to measure entanglement and R\'enyi entropies by
relating them to $U(1)$ charges fluctuating in and out of a subregion, for
systems equivalent to non-interacting fermions.
  From our analysis, we find universal features in conformal field theories, in
particular the area dependence of the capacity of entanglement appears to track
that of the entanglement entropy. This relation is seen to be modified under
perturbations from conformal invariance. In quenched 1+1 dimensional CFTs, we
compute the rate of growth of the capacity of entanglement. The result may be
used to refine the interpretation of entanglement spreading being carried by
ballistic propagation of entangled quasiparticle pairs created at the quench.
