Meaning of the term "phase" in chemistry and thermodynamics I have some doubts about the definition of the term “phase” in chemistry and thermodynamics (is the meaning the same?).
The "textbook" definition is:
"A phase is a form of matter that is uniform throughout in both chemical composition and physical state."
Does physical state means macroscopic intensive proprieties, like temperature? So a body with a temperature gradient doesn't have a phase? Is the term “phase” only significant at equilibrium?
And does “same chemical composition” means same chemical formula or same concentration? In the first case a solution would have two phases, in the second only one.
 A: 
The "textbook" definition is: "A phase is a form of matter that is uniform throughout in both chemical composition and physical state."
Does physical state means macroscopic intensive proprieties, like temperature?

That's one textbook's definition, not "the" textbook definition. Other textbooks have other definitions.
Consider water held at it's triple point. At this point, some of the water will be liquid, some will be solid, and some will be gaseous. All three phases have the same uniform chemical composition, the same temperature, and the same pressure. Uniformity in temperature not what is meant by "physical state" in this context.
The intent of the term "physical state" is to capture concepts such as solidity vs liquidity vs gaseousness, thermal and electrical conductivity, crystalline structure, transitions that generate or consume heat, etc. However, poking at the concept of "phase of matter" hard enough makes the concept breaks down a bit. For example, by going around the critical point, a liquid transitions to a gas without going through a phase transition. The distinction between a gas and a plasma is fuzzier yet.
A: @David Hammen
So to summarize, correct me if I'm wrong.
From a microscopic point of view we can say that a phase is a set of particles (atoms or molecules) of same type held together in the same way (same structure, same type of bonds). 
From a macroscopic point of view a phase is a portion of matter the proprieties of which don’t depend on the spatial coordinates. By proprieties I mean anything that is definite from a phenomenological perspective (anything I’ve a meaningful procedure to observe and measure).
The two view should be consistent (I think). If we go with this interpretation a phase is not defined by continuity but by uniformity. Meaning that if a propriety change with continuity we have infinite phases. This would also be coherent with the way thermodynamics looks at this kind of systems (they have to be broken down in parts small enough to be considered homogeneous otherwise we can’t talk of a “state”).
A: In thermodynamics when we talk about phase we mean the phases like liquid, solid and gas. 
In chemistry one can have phases which refer to the crystal structure of materials for example in perovskites, the orthorhombic and tetragonal phases are most common non-cubic variants.
Mixed throughout, as inn general language, we sometimes talk of a phase of a process. A certain phase might take place in the gradual development of something.
So, no - the meaning of the word phase in thermodynamics and chemistry is not uniform. 
