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"Entropy" and "action" are two entirely different concepts. The first relates to a coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.

Also note that: 1) the second law of thermodynamics tells us entropy doesn't decrease, it need not increase and certainly can attain non-maximal values, and 2) action is stationary and not necessarily minimal or maximal. Hence, when considered as fundamental physics laws, both 'maximal entropy' and the 'principle of least action' are misnomers.

Zooming in to the core of your question: 'entropy non-decrease' and 'action stationarity' are unrelated, and one can not be derived from the other. This is for the simple reason that 'action stationarity' describes a reversible physics, while 'entropy non-decrease' presents us with an irreversible picture of evolution of physical systems. The difference, again, is in microscopic versus macroscopic.

As an analogy, think about two statements one can make about the physics of pool billiard. The first being that the balls collide according to Newtons laws which can be expressed by stating that the detailed balls trajectories render a quantity called 'action' stationary. The second being the coarse-grained statistical statement that as long as balls aren't pocketed yet, the mean distance between the balls doesn't decrease. Both statements are unrelated and apply to a description of pool billiard at different levels.

"Entropy" and "action" are two entirely different concepts. The first relates to a coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.

Also note that: 1) the second law of thermodynamics tells us entropy doesn't decrease, it need not increase and certainly can attain non-maximal values, and 2) action is stationary and not necessarily minimal or maximal. Hence, when considered as fundamental physics laws, both 'maximal entropy' and the 'principle of least action' are misnomers.

Zooming in to the core of your question: 'entropy increase' and 'action stationarity' are unrelated, and even incompatible. One certainly can not be derived from the other. This is for the simple reason that 'action stationarity' describes a reversible physics, while 'entropy increase' presents us with an irreversible picture of evolution of physical systems. The difference, again, is in microscopic versus macroscopic.

As an analogy, think about two statements one can make about the physics of pool billiard. The first being that the balls collide according to Newtons laws which can be expressed by stating that the detailed balls trajectories render a quantity called 'action' stationary. The second being the coarse-grained statistical statement that as long as balls aren't pocketed yet, the mean distance between the balls doesn't decrease. Both statements are unrelated and apply to a description of pool billiard at different levels.

"Entropy" and "action" are two entirely different concepts. The first relates to a coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.

Also note that: 1) the second law of thermodynamics tells us entropy doesn't decrease, it need not increase and certainly can attain non-maximal values, and 2) action is stationary and not necessarily minimal or maximal. Hence, when considered as fundamental physics laws, both 'maximal entropy' and the 'principle of least action' are misnomers.

Finally, 'entropy non-decrease' and 'action stationarity' are unrelated, and one can certainly not be derived from the other. This is for the simple reason that 'action stationarity' describes a reversible physics, while 'entropy non-decrease' presents us with an irreversible picture of evolution of physical systems. The difference, again, is in microscopic versus macroscopic.

As an analogy, think about two statements one can make about the physics of pool billiard. The first being that the balls collide according to Newtons laws which can be expressed by stating that the detailed balls trajectories render a quantity called 'action' stationary. The second being the coarse-grained statistical statement that as long as balls aren't pocketed yet, the mean distance between the balls doesn't decrease. Both statements are unrelated and apply to a description of pool billiard at different levels.

"Entropy" and "action" are two entirely different concepts. The first relates to a coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.

Also note that: 1) the second law of thermodynamics tells us entropy doesn't decrease, it need not increase and certainly can attain non-maximal values, and 2) action is stationary and not necessarily minimal or maximal. Hence, when considered as fundamental physics laws, both 'maximal entropy' and the 'principle of least action' are misnomers.

Zooming in to the core of your question: 'entropy non-decrease' and 'action stationarity' are unrelated, and one can not be derived from the other. This is for the simple reason that 'action stationarity' describes a reversible physics, while 'entropy non-decrease' presents us with an irreversible picture of evolution of physical systems. The difference, again, is in microscopic versus macroscopic.

As an analogy, think about two statements one can make about the physics of pool billiard. The first being that the balls collide according to Newtons laws which can be expressed by stating that the detailed balls trajectories render a quantity called 'action' stationary. The second being the coarse-grained statistical statement that as long as balls aren't pocketed yet, the mean distance between the balls doesn't decrease. Both statements are unrelated and apply to a description of pool billiard at different levels.

"Entropy" and "action" are two entirely different concepts. The first relates to coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.

Also note that: 1) the second law of thermodynamics tells us entropy doesn't decrease, it need not increase and certainly can attain non-maximal values, and 2) action is stationary and not necessarily minimal or maximal. Hence, when considered as fundamental physics laws, both 'maximal entropy' and the 'principle of least action' are misnomers.

Finally, 'entropy non-decrease' and 'action stationarity' are unrelated, and one can certainly not be derived from the other. This is for the simple reason that 'action stationarity' describes a reversible physics, while 'entropy non-decrease' presents us with an irreversible picture of evolution of physical systems. The difference, again, is in microscopic versus macroscopic.

As an analogy, think about two statements one can make about the physics of pool billiard. The first being that the balls collide according to Newtons laws which can be expressed by stating that the detailed balls trajectories render a quantity called 'action' stationary. The second being the coarse-grained statistical statement that as long as balls aren't pocketed yet, the mean distance between the balls doesn't decrease. Both statements are unrelated and apply to a description of pool billiard at different levels.

"Entropy" and "action" are two entirely different concepts. The first relates to a coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.

Also note that: 1) the second law of thermodynamics tells us entropy doesn't decrease, it need not increase and certainly can attain non-maximal values, and 2) action is stationary and not necessarily minimal or maximal. Hence, when considered as fundamental physics laws, both 'maximal entropy' and the 'principle of least action' are misnomers.

Finally, 'entropy non-decrease' and 'action stationarity' are unrelated, and one can certainly not be derived from the other. This is for the simple reason that 'action stationarity' describes a reversible physics, while 'entropy non-decrease' presents us with an irreversible picture of evolution of physical systems. The difference, again, is in microscopic versus macroscopic.

As an analogy, think about two statements one can make about the physics of pool billiard. The first being that the balls collide according to Newtons laws which can be expressed by stating that the detailed balls trajectories render a quantity called 'action' stationary. The second being the coarse-grained statistical statement that as long as balls aren't pocketed yet, the mean distance between the balls doesn't decrease. Both statements are unrelated and apply to a description of pool billiard at different levels.