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The fluctuation-dissipation relation for the classical definition of work isextended to thermally isolated systems, in classical and quantum realms. Fromthis, the optimal work variance is calculated, showing it achieves its minimumpossible value, independent of the rate of the process, in a so-calledquasistatic variance, related to the difference between the quasistatic workand the difference of Helmholtz's free energy of the system. The result iscorroborated by the example of the classical and driven harmonic oscillator,whose probability density function of the work distribution is non-Gaussian andconstant for different rates. The optimal variance is calculated for thequantum Ising chain as well, showing its finiteness if the linear responsevalidity criterion is complied with. A stronger definition of the arbitraryconstant for the relaxation function of thermally isolated systems is obtainedalong the work.

Optimal work fluctuations for thermally isolated systems in weak processes