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The distributions of work for strongly non-equilibrium processes are studiedusing a very general form of a large-deviation approach, which allows one tostudy distributions of almost arbitrary quantities of interest for equilibrium,non-equilibrium stationary and even non-stationary processes. The method isapplied to varying quickly the external field in a wide range B=3 <-> 0 forcritical (T=2.269) two-dimensional Ising system of size LxL=128x128. To obtainfree energy differences from the work distributions, they must be studied inranges where the probabilities are as small as 10^{-240}, which is not possibleusing direct simulation approaches. By comparison with the exact free energies,which are available for this model for the zero-field case, one sees that thepresent approach allows one to obtain the free energy with a very high relativeprecision of 10^{-4}. This works well also for non-zero field, i.e., for a casewhere standard umbrella-sampling methods seem to be not so efficient tocalculate free energies. Furthermore, for the present case it is verified thatthe resulting distributions of work for forward and backward process fulfillCrooks theorem with high precision. Finally, the free energy for the Isingmagnet as a function of the field strength is obtained.

Generalized black-box large deviation simulations: High-precision work distributions for extreme non-equilibrium processes in large systems