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1.Energy is conserved in the isolated system

2.Entropy in isolated non quasi static systems will always tend to increase.

Lets take a brief look at Noethers theorem:

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

Now without entering the mathematics. conservation of energy is a because of invariance under time translations.That is the langragian is not explicitly depending on time energy is conserved.

Without entering the mathematics, lets assume that we are in a system such that the above assumption is thrown out of the window.Would that mean that temperature does not need to flow from high temperatures to low temperatures?