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While reading Kardar's 'Statistical Physics of Particles', in section explaining Zeroth law of Thermodynamics, Kardar claims that each of the system's i.e A & B , B & C are assumed to be separately in mechanical equilibrium. If they are allowed to do work on each other, additional conditions like constant pressure is required to describe their joint mechanical equilibrium?

But how can just constant pressure ensure that they are in mechanical equilibrium, shouldn't the process be carried out quasi statically and no friction should be present if it is some kind of a gas-piston systems?

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Equal pressure is a necessary but not sufficient condition for mechanical equilibrium. If systems with different pressures are placed in contact then the pressure difference will result in net forces between them, and so they are not in equilibrium.

If the systems are initially at rest and the mechanical state of the systems is characterized by a single coordinate (and if we can reasonably take that coordinate to be the volume) then equal pressure is also sufficient for mechanical equilibrium, essentially because that is the definition of pressure.

If your system has more complicated mechanical degrees of freedom then the conditions for mechanical equilibrium will be correspondingly more complex, until you reach the general definition given in classical mechanics.

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