Microcanonical temperatures�defined as the �tangential� (T� = [?U/?S�]N,V) or �discrete� (Td� = [?U/?S�]N,V) slopes of U vs. S profiles�can be employed in studies of small, isolated and/or non-equilibrium systems. We compare the dependence of T� and Td� of paramagnetic spin lattices (PSLs) on magnetic field strength and number of spins N to those of the �tangential� (Tc = [?U/?Sc]N,V) and �discrete� (Tdc = = [?U/?Sc]N,V) canonical temperatures. We demonstrate that the sign, magnitude, field� and size�dependence of T�, Td�, and Tdc closely mimic those of Tc, indicating that T�, Td� and Tdc, are legitimate measures of temperature, and that the four temperatures are non-intensive and the microcanonical and canonical entropies S� and Scare non-extensive for small (N = 1015) PSLs. The entropies converge and become extensive in the thermodynamic limit. We detail the origin of the non-extensive entropies, as they indicate that small PSLs violate Boltzmann statistics.

Comparison of microcanonical and canonical temperatures in paramagnetic spin lattices and other two-level systems

246th National Meeting (2013)

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