Zusammenfassung
The distribution functions of the work performed on a two
dimensional Ising model under the influence of an external magnetic
field which is switched on and off are studied.
These distributions are calculated by means of Monte
Carlo simulations for temperatures below and above, as well as close to
the critical temperature, $T_c$, and for different rates
of the switching processes. For this system the Jarzynski and the
Crooks Fluctuation Theorems are verified. It is found that
Crooks Fluctuation Theorem provides a faster method to evaluate free
energy differences in this system with respect to the Jarzynski
equality. As expected, for temperatures far from $T_c$ the convergence
of the results is faster than for $T T_c$, where a slower
switching rate is needed. Results obtained from the theorems of Crooks
and Jarzynski are compared with thermodynamic integration calculations
and it is find that they agree very well within error bars.
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