  The notion of capacity of entanglement is the quantum information theoretic
counterpart of the heat capacity which is defined as the second cumulant of the
entanglement spectrum. Given any bipartite pure state, we can define the
capacity of entanglement as the variance of the modular Hamiltonian in the
reduced state of any of the subsystems. Here, we study the dynamics of this
quantity under non-local Hamiltonian. Specifically, we address the question:
Given an arbitrary non-local Hamiltonian what is the capacity of entanglement
that the system can possess? As an useful application, we show that the quantum
speed limit for creating the entanglement is not only governed by the
fluctuation in the non-local Hamiltonian, but also depends inversely on the
time average of square root of the capacity of entanglement. Furthermore, we
discuss this quantity for a general self-inverse Hamiltonian and provide a
bound on the rate of the capacity of entanglement. Towards the end, we
generalise the capacity of entanglement for bipartite mixed states based on the
relative entropy of entanglement and show that the above definition reduces to
the capacity of entanglement for pure bipartite states. Our results can have
several applications in diverse areas of physics.
