  Traditionally, it is understood that fluctuations in the equilibrium
distribution are not evident in thermodynamic systems of large $N$ (the number
of particles in the system) \cite{Huang1}. In this paper we examine the
validity of this perception by investigating whether such fluctuations can in
reality depend on temperature.
  Firstly, we describe fluctuations in the occupation numbers of the energy
levels for an isolated system, using previously unknown identities that we have
derived for the purpose, which allow us to calculate the moments of the
occupation numbers. Then we compute analytically the probability distribution
of these fluctuations. We show that, for every system of fixed and finite $N$,
fluctuations about the equilibrium distribution do, in fact, depend on the
temperature. Indeed, at higher temperatures the fluctuations can be so large
that the system does not fully converge on the Maxwell-Boltzmann distribution
but actually fluctuates around it. We term this state, where not one macrostate
but a region of macrostates closely fit the underlying distribution, a ``{\it
fluctuating equilibrium}''. Finally, we speculate on how this finding is
applicable to networks, financial markets, and other thermodynamic-like
systems.
