  In this work, we discuss the implications of a recently obtained equilibrium
fluctuation-dissipation relation on the extension of the available Monte Carlo
methods based on the consideration of the Gibbs canonical ensemble to account
for the existence of an anomalous regime with negative heat capacities $C<0$.
The resulting framework appears as a suitable generalization of the methodology
associated with the so-called \textit{dynamical ensemble}, which is applied to
the extension of two well-known Monte Carlo methods: the Metropolis importance
sample and the Swendsen-Wang clusters algorithm. These Monte Carlo algorithms
are employed to study the anomalous thermodynamic behavior of the Potts models
with many spin states $q$ defined on a $d$-dimensional hypercubic lattice with
periodic boundary conditions, which successfully reduce the exponential
divergence of decorrelation time $\tau$ with the increase of the system size
$N$ to a weak power-law divergence $\tau\propto N^{\alpha}$ with
$\alpha\approx0.2$ for the particular case of the 2D 10-state Potts model.
