  In this paper, we analyze dissipative diamagnetism, arising due to
dissipative cyclotron motion in two dimensions, in the light of the quantum
counterpart of energy equipartition theorem. We consider a charged quantum
particle moving in a harmonic well, in the presence of a uniform magnetic
field, and coupled to a quantum heat bath which is taken to be composed of an
infinite number of independent quantum oscillators. The quantum counterpart of
energy equipartition theorem tells us that it is possible to express the mean
kinetic energy of the dissipative oscillator as a two-fold average, where, the
first averaging is performed over the Gibbs canonical state of the heat bath
while the second one is governed by a probability distribution function
$P_k(\omega)$. We analyze this result further, and also demonstrate its
consistency in the weak-coupling limit. Following this, we compute the
equilibrium magnetic moment of the system, and reveal an interesting connection
with the quantum counterpart of energy equipartition theorem. The expressions
for kinetic energy and magnetic moment are reformulated in the context of
superstatistics, i.e. the superposition of two statistics. A comparative study
of the present results with those obtained from the more traditional Gibbs
approach is performed and a perfect agreement is obtained.
