COMMENTS ON “THERMODYNAMIC UNCERTAINTY RELATIONS” BY J. UFFINK AND J. VAN LITH

Fundamental errors in the Uffink and van Lith paper [Found. Phys.29, 655-92 (1999)] are highlighted. Contrary to their claim, thermodynamic uncertainty relations are derived from the second law. To first order in the energy difference, the increase in entropy when two systems at slightly different temperatures are placed in thermal contact is equal to the product of the second subsystems multiplied by the change in energy of the first subsystem. This expression for the increase in entropy has the same range of validity as the thermodynamic uncertainty relations and the Fisher information, i.e., they are second order quantities. The dispersion in the inverse temperature of either subsystem cannot be less than the inverse of the Fisher information, or the inverse of the dispersion in energy of the composite system at the lowest possible equilibrium temperature, where the equality applies strictly to reversible processes and the inequality to irreversible ones.