Evolution rate of thermodynamic systems

Time is absent in the common idea of classical thermodynamics; instead it is always ideally present considering work and heat exchanged or state functions change. In irreversible thermodynamic time seems to be considered and rate of change is introduced. Actually time is often not at the attention focus when searching for law to understand the system's evolution. A proposal to introduce the time in thermodynamics trough the classical Hamilton's principle, shows a possible interpretation of some process in an unified principle considering MaxEP and minimum evolution time for systems. At the same time it is evidenced that the irreversibility contribute to the slowing down of natural phenomen