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In classical thermodynamics, mechanical equilibrium is defined as

the state of a system in which there is no net flow of volume as there should be no net pressure within the system.

Ok. Understood. Within the system,there should be no net force and hence no net flow of matter.

But, how can it be defined in Statistical-mechanics? What is the cause for mechanical equilibrium at a microscopic level of the system?

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  • $\begingroup$ It is not entirely clear what you mean by microscopic in this context. Should the answer not be basically the same: that there is no net flow of molecules? $\endgroup$
    – alarge
    Commented Jan 8, 2015 at 21:56

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Macroscopically, mechanical equilibrium is due to friction.

Microscopically, one popular view is that friction is only macroscopic manifestation of immense number of variables and is explained by probabilistic considerations - it is much more probable for particles to decorrelate and energy to dissipate into chaotic thermal motion of particles than for the particles to correlate and energy appear in the form of macroscopically visible motion.

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  • $\begingroup$ How is mechanical equilibrium due to friction? $\endgroup$
    – gented
    Commented Jul 5, 2015 at 22:44
  • $\begingroup$ Consider, for example, pendulum in gravity field. When set in motion, it oscillates back and forth but due to friction in the axis and the air, it eventually stops moving and settles down in equilibrium position. $\endgroup$ Commented Jul 6, 2015 at 0:36
  • $\begingroup$ It does not oscillate due to friction in the axes and air; it oscillates due to gravity. If there were any other force evening gravity out than it would be in mechanical equilibrium, but no friction is required to do so. Maybe you are making confusion between mechanical equilibrium and the equilibrium of the oscillations around a given point, which are two different things. $\endgroup$
    – gented
    Commented Jul 6, 2015 at 0:43
  • $\begingroup$ 1) I did not write the pendulum oscillates due to friction. 2) Without friction, if the gravity was evened out, the pendulum could still move perpetually. Only if friction is present, the motion of the pendulum eventually stops and the system settles down in state of mechanical equilibrium. $\endgroup$ Commented Jul 6, 2015 at 0:55
  • $\begingroup$ Yes, but that is only one example of mechanical equilibrium. You may have mechanical equilibrium also without friction, that was my point. $\endgroup$
    – gented
    Commented Jul 6, 2015 at 1:01

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