I'm taking a course about statistical mechanics and it is completely new to me . We've learned about entropy and how when 2 different sub-systems comes to contact the entropy of the whole system keeps growing until it reaches its maximum ,then he defined the temperature of each of the 2 sub-systems to be the inverse of the derivative of entropy in relation to its energy and said that the whole system reaches its maximum entropy when both of the sub-systems have the same temperature . Now I want to ask, according to this mathematical definition of temperature , what is the physical meaning and definition of temperature and what does it mean when temperature reaches zero or infinity ?BONUS QUESTION ,if the whole system reaches its maximum entropy then it means its temperature goes to infinity but at the same time its sub-systems have finite temperature how is that ?
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