The maximum entropy and least action principles have been discussed by many researchers in various fields such as thermodynamics, classical physics, quantum mechanics, and quantum electrodynamics. Both principles suggest that the basic laws of nature can be derived by optimizing certain properties of dynamic systems. This raises an important question on the possible connections between these principles. What can be learned from such connections and/or correlations?
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"Maximum entropy production principle in physics, chemistry and biology"
the method of maximum entropy change is in accordance with the principle of maximum entropy which can be used for nonequilibrium systems when available. If the system of interest occupying the two phase volumes is in equilibrium, then maximum entropy change of dynamic process linking the phase volumes naturally leads to the Jaynes’ principle of maximum entropy for equilibrium systems, as discussed
Article Maximum Entropy Change and Least Action Principle for Nonequ...
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
Following function remains "stationary" for entropy maximization in quantum statistical mechanics,
Q= ln Z - λ d/dλ ln Z, where λ= 1 / iħ , Z is partition function which is defined as an integral over histories of an exponential function of action.
Ref. Baez and Pollard arxiv [arXiv:1311.0813]
If we think classically, entropy change is an irreversible process whereas Lagrangian and Hamiltonian dynamics deals with reversible processes. Then they are two areas of Physics which are mutually disjoint.
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