Thermodynamic irreversibility: what is it and where does it come from?

The entropic irreversibility of thermnodynamic descriptions of fluid behavior is often contrasted with the dynamical reversibility of the underlying molecular model. There is no conflict, however, if we distinguish among different kinds of irreversibility. The thermodynamic kind is not opposed to dynamical reversibility. It is a directional irreversibility that is a common feature of stochastic descriptions arising from the excessive time symmetry of such descriptions; entropy is created in both directions of time. Symmetric stochastic descriptions can be compatible with asymmetric dynamical descriptions for one direction of any fluid process but not in the other direction. The origin of thermodynamic irreversibility in the dynamical molecular model is a constraint on initial conditions that rules out the non-stochastic direction. The constraint materializes in any molecular model for any number of molecules whenever the times between changes of external conditions are short compared to the lengths of equilibrium intervals. In the case of an observable fluid the equilibrium intervals are overwhelmingly larger than the times between interruptions and the fluid is maintained in a condition of having a quickly interrupted equilibrium in its recent past. This guarantees the randomness that permits a stochastic description but it does not imply that the actual fluid behavior is symmetric in time. If time were reversed the fluid process would certainly be reversed and it would not obey the second law