The Multifractal Time and Irreversibility in Dynamic Systems
  The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last depends on densities of Lagrangians in a given time moment and in a given point of space. After transition to sets of time points with the integer dimension the obtained equations transfer in the known equations of classical dynamics. Production of an entropy is not equally to zero in space with multifractal time, i.e. the classical systems in this space are non-closed. 
L.Ya.Kobelev