On the Thermodynamics of Classical Micro-Canonical Systems

We give two arguments why the thermodynamic entropy of non-extensive systems involves R´enyi’s entropy function rather than that of Tsallis. The first argument is that the temperature of the configurational subsystem of a mono-atomic gas is equal to that of the kinetic subsystem. The second argument is that the instability of the pendulum, which occurs for energies close to the rotation threshold, is correctly reproduced