A compromised arrow of time
  The second law of thermodynamics - the usual statement of the arrow of time - has been called the most fundamental law of physics. It is thus difficult to conceive that a single dynamical system could contain subsystems, in significant mutual contact, possessing opposite thermodynamic arrows of time. By examining cosmological justification for the usual arrow it is found that a consistent way to establish such justification is by giving symmetric boundary conditions at two (cosmologically remote) times and seeking directional behavior in between. Once this has been demonstrated, it is seen that entropy increase can be reversed and that the usual arrow is less totalitarian than previously believed. In the same vein, other boundary conditions, modeling shorter periods in the evolution of the cosmos, can be found that allow the simultaneous existence of two thermodynamic arrows, notwithstanding moderate interaction between the systems possessing those arrows. Physical consequences of the existence and detection of opposite-arrow regions are also considered. 
L. S. Schulman