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I have been confused at points due to multiple uses of the word "phase".

  • Mainly, when I think of a phase diagram, I think of a graph relating temperature to pressure, and segments the possible combinations of these values into regions in which a particular substance is "solid", "liquid", etc.

  • This is something completely different from phase space, in the dynamical systems sense, where each point in the space represents the state of a dynamical system.

  • There are also notions of phase and phase velocity.

Am I correct in assuming that the words "phase" in these contexts have nothing to do with each other, and are there other meanings that I shouldn't conflate?

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Right. Other than the generic meaning of phase being the state of a system, these two specific meanings are independent. As a third example, the phase associated with wave motion would be another separate definition.

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The world phase comes from the greek phasys (ϕάσις), meaning "appearence", from the verb ϕαίνομαι, "to appear", "to show one self".

Therefore, you are correct when you say that the meaning of the word "phase" is different in the three cases you cited, but they all have in common the concept of appearence, state: the thermodynamic state in the phase diagram, the dynamical state un the phase space, and the "oscillation state" in a wave.

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