  One approach is to deny the time asymmetry of the dynamics governing the micro-constituents and to look for a replacement law that is itself time asymmetric.  A modern version of this looks to an interpretation of quantum mechanics that seeks to explain the notorious “collapse of the wave packet” upon measurement.  Ghirardi, Rimini and Weber (GRW) have posited the existence of a purely stochastic process deeper than that of the usual quantum evolution. This pure chance process will quickly drive macroscopic systems into near eigenfunctions of position while leaving isolated micro-systems in superposition states.  The stochastic process is asymmetric in time (as is the collapse of the wave function upon measurement).  D. Albert has suggested that such a GRW process, if real, might also be invoked to account for the time asymmetry of the dynamics of systems that needs to be accounted for in thermodynamics.  The time asymmetry of the GRW collapse might work by directly affecting the dynamics of the system, or it might do its job by appropriately randomizing the initial states of isolated systems.  Little has yet been done to fill in the details to see if the posited GRW processes could, if real, account for the know thermodynamic asymmetries.  And, of course, there is much skepticism that the GRW processes are even real.