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Why a quasi static process require large temperature gradient?​

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A quasi-static process is often defined as a process "that occurs infinitely slowly such that equilibrium HOLDS at all times."(Harvard, Matthew Schwartz, statistical mechanics Spring 2019). My question is a simple but possibly subtle one which I haven't SEEN mentioned anywhere.A quasi-static process is often defined as a process "that occurs infinitely slowly such that equilibrium holds at all times."(Harvard, Matthew Schwartz, statistical mechanics Spring 2019). My question is a simple but possibly subtle one which I haven't seen mentioned anywhere.Simply PUT, does the system need to maintain equilibrium with the surroundings at all times during the process in order for the process to be CLASSIFIED as a quasi-static process or is the lesser requirement of simply having the system maintain INTERNAL equilibrium with itself good enough to classify the process as quasi-static



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