What is the difference between a mixture and a compound?

According to most textbooks:

• a compound is an entity consisting of two or more atoms, commonly from different chemical elements, which associate via chemical bonds.
• On the other hand, a mixture is a material made up of two or more different substances which are mixed but are not combined chemically.

So the difference is that a mixture refers a physical combination of substances, whereas a compound refers to a chemical combination.

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But these definitions do not say anything unless we establish the difference between a chemical and a physical combination and, according to the same textbooks:

• a chemical process is a method or means of somehow changing one or more compounds,
• whereas physical changes are changes affecting a substance, but not its chemical composition, because they do not change chemical bonding.

As you probably have already realized, the definitions are circular! We put two substances together. If the process is not chemical, what we obtain is a mixture, not a compound. But we defined a non-chemical process as the one where the compounds are still the same compounds, but mixed. Who is Alice? She is Bob's cousin. And who is Bob? Alice's cousin. We still do not know who is Alice!

Are you able to give a definition of compounds and mixtures that is not circular? How can we define chemical process without saying that a chemical process is different from a physical one in that compounds change?

Notice the distinction cannot come from the physical properties if the substance, because the physical properties of a mixture may differ from those of the components. In addition, evolved or absorbed heat cannot be the solution because, both in chemical reactions and in mixtures, heat is either evolved (an exothermic process) or absorbed (an endothermic process).

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers.