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The topological effects on the thermal properties of several knotconfigurations are investigated using Monte Carlo simulations. In order tocheck if the topology of the knots is preserved during the thermal fluctuationswe propose a method that allows very fast calculations and can be easilyapplied to arbitrarily complex knots. As an application, the specific energyand heat capacity of the trefoil, the figure-eight and the $8_1$ knots arecalculated at different temperatures and for different lengths. Short-rangerepulsive interactions between the monomers are assumed. The knotsconfigurations are generated on a three-dimensional cubic lattice and sampledby means of the Wang-Landau algorithm and of the pivot method. The obtainedresults show that the topological effects play a key role for short-lengthpolymers. Three temperature regimes of the growth rate of the internal energyof the system are distinguished.

Topological effects in the thermal properties of knotted polymer rings