Five previously unknown inequalities relating equilibrium free energydifferences and non-equilibrium work fluctuations are derived, and lucid pathto derivation of many similar inequalities is presented. These results arebased upon combined exploitation of the Jarzynski equality and thegeneralization of the scheme for producing uncertainty-type inequalities due toH. Weyl. The inequalities may possibly lead to better understanding of behaviorof the equilibrium free-energy estimators from non-equilibrium experimentaldata in many important applications concerning biological, chemical, andphysical molecular processes.
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