In what ways can entropy of the universe increase? So far, I have been able to come across two scenarios in which entropy of the universe increases. First, when heat flows at a finite temperature gradient and second, during expansion of air particles into a vacuum (Joule's Expansion). Is there any other way in which entropy can increase? I'm assuming that there should be because neither of the above instances explains why entropy should increase during irreversible adiabatic compression. Considering an ideal case and neglecting entropy generation due to turbulence, there must be something $fundamentally$ different about irreversible adiabatic compression that generates entropy. Right? 
 A: Bird, Stewart, and Lightfoot, Transport Phenomena, in Chapter 11, problem 11D.1 (Equation of change for entropy) discuss the fundamental causes of entropy generation/irreversibility.  They identify heat flows at finite temperature gradients, viscous dissipation of mechanical energy (associated with viscous stresses resulting from rapid fluid deformation), and, in a later chapter, diffusive mass transfer at finite concentration gradients.  The example you gave for Joule Thompson falls under the category of viscous dissipation; this also covers entropy generation associated with rapid adiabatic compression of a gas.  For Newtonian fluids (such as air and non-polymeric liquids), the rate of entropy generation per unit volume from viscous dissipation is equal to the viscosity times the square of the "effective" velocity gradient, divided by the absolute temperature.  
I recommend that you study the development in this example in Bird et al carefully.  I personally found it extremely enlightening, and it cleared up all my gaps in understanding.
