Entropic Measure of Time, and Gas Expansion in Vacuum
  The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is introduced with the help of Boltzmann's classic entropy. It is shown that, in the general case, this measure of time proves to be nonlinearly related to the reference measure assumed uniform by convention. The connection between this result and the results of other authors investigating measure of time in some biological and cosmological problems is noted. 
Leonid M. Martyushev, Evgenii V. Shaiapin
cond-mat.stat-mech gr-qc physics.class-ph