Zeroth law of thermodynamics in terms of heat

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The zeroth law of thermodynamics establishes a foundational principle regarding thermal equilibrium, stating that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. It implies that energy transfer between two systems occurs only when they are not in thermal equilibrium. When one system transfers energy to another, it indicates a difference in temperature, confirming they are not in thermal equilibrium. Thus, the concept of heat is integral to understanding the zeroth law, as it relates to energy transfer. The discussion emphasizes the necessity of thermal non-equilibrium for energy transfer to take place.
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Is there any definition of the zeroth law of termodynamics using the heat concept?

And does the zeroth law imply that the only way 2 systems can transfer energy is if they're not in thermal equilibrium? If 1 system is transferring energy to another one, that means they're not in thermal equilibrium right?
 
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Yes.
 

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