Now that's a great question.

The many physical phenomena of interest that involve

quasi-thermodynamic processes that are slightly out of equilibrium.

Let's take some examples.

Now, heat transport by the internal motions in a material,

driven by a temperature imbalance.

Now electric currents, carried by the motion of charges,

in a conductor, driven by a voltage imbalance.

Spontaneous chemical reactions, driven by a decrease in free energy.

Friction, dissipation, quantum decoherence, and so on.

Now all of these processes occur over time with characteristic rates.

And these rates are of crucial importance in engineering.

Now, the field of what is called

Non-equilibrium Statistical Thermodynamics concerns itself with

understanding these non-equilibrium processes at the microscopic level.

Now, Statistical Thermodynamics, the way we have learned it can only

be used to calculate the final result after all these external imbalances

have been removed and the ensemble settles back in equilibrium.

In principle, Non-equilibrium Statistical Thermodynamics could be exact and

ensembles, for instance, for an isolated system could be evolved over time

according to the doministic equations such as the Louisville's Theorem, or

the Quantum Mechanical Version, the Fornierian Equation.

Now, in order to make headway in to modeling this irreversible processes its

necessary to add additional ingredients besides probability and

reversible mechanics.

Now, Non-equilibrium Statistical Thermodynamics is therefore still

an active area of theoretical research as the range

of validity of these additional assumptions continue to be explored.