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This is in answer to (primarily) the third question. The association with disorder is naturally anthropocentric, "disorder" is an idea based on our experience of the world.

  The association with "disorder" is straightforward once "order" is properly defined, which, given the number of meanings attributed to the word, is not entirely trivial. From Merriam-Webster, this seems to most closely fit the intended meaning when used in chemical circles:

a regular or harmonious arrangement

Regularity always implies lower entropy, all else being equal. It is therefore fair to associate "order" with lower entropy.

The association with "order" or regularity also syncs with the concept of entropy as far as the statistical mechanical definition following Boltzmann $$S= k_\mathrm B \log \Omega$$ is concerned. $\Omega$, the number of microstates available to the system, is quantified by the entropy. More possible different microstates means higher entropy. Solids are usually more regular and therefore have lower entropy than fluid states at the same T. Same when comparing gases and liquids. The possible microstates increases from solid to liquid to gas.

This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system. You need more information to describe all possible arrangements of molecules in a gas or liquid than in a solid.

The association of entropy with disorder is anthropocentric. "Disorder" is a concept derived from our experience of the world. The association with "disorder" is clearer once we explain what we mean by "order". The following definition among those provided by Merriam-Webster most closely fits the intended meaning:

a regular or harmonious arrangement

Since regularity always implies lower entropy, all else being equal, it is therefore fair to associate "order" with lower entropy.

The association with "order" or regularity also syncs with the concept of entropy according to Boltzmann's statistical mechanical definition ($S= k_\mathrm B \log \Omega$). $\Omega$, the number of microstates available to the system, can be quantified using the entropy. More possible unique microstates implies a higher entropy. Greater regularity implies more constraints regarding arrangement of the system and therefore less possible microstates. Solids are usually more regular and therefore have lower entropy than fluid states at the same T. Same when comparing gases and liquids. The possible microstates increases from solid to liquid to gas.

This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system. You need more information to describe all possible arrangements of molecules in a gas or liquid than in a solid. Think of entropy as measuring the length of the recipe required to build all possible arrangements of the system.

This is in answer to (primarily) the third question. The association with disorder is naturally anthropocentric, "disorder" is an idea based on our experience of the world, but it does synch with the concept of entropy as far as the statistical mechanical definition following Boltzmann $$S= k_\mathrm B \log \Omega$$ is concerned. $\Omega$, the number of microstates available to the system, is quantified by the entropy. More possible different microstates means higher entropy.

The association with "disorder" is straightforward once "order" is properly defined, which, given the number of meanings attributed to the word, is not entirely trivial. From Merriam-Webster, this seems to fit the intended definition most closely when used in chemical circles  :

a regular or harmonious arrangement

Regularity always implies lower entropy, all else being equal. It is therefore fair to associate "order" with lower entropy. This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system.

This is in answer to (primarily) the third question. The association with disorder is naturally anthropocentric, "disorder" is an idea based on our experience of the world.

The association with "disorder" is straightforward once "order" is properly defined, which, given the number of meanings attributed to the word, is not entirely trivial. From Merriam-Webster, this seems to most closely fit the intended meaning when used in chemical circles:

a regular or harmonious arrangement

Regularity always implies lower entropy, all else being equal. It is therefore fair to associate "order" with lower entropy.

The association with "order" or regularity also syncs with the concept of entropy as far as the statistical mechanical definition following Boltzmann $$S= k_\mathrm B \log \Omega$$ is concerned. $\Omega$, the number of microstates available to the system, is quantified by the entropy. More possible different microstates means higher entropy. Solids are usually more regular and therefore have lower entropy than fluid states at the same T. Same when comparing gases and liquids. The possible microstates increases from solid to liquid to gas. 

This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system. You need more information to describe all possible arrangements of molecules in a gas or liquid than in a solid.

This is in answer to (primarily) the third question. The association with disorder is naturally anthropocentric, "disorder" is an idea based on our experience of the world, but it does synch with the concept of entropy as far as the statistical mechanical definition following Boltzmann $$S= k_B \log \Omega$$ is concerned. $\Omega$, the number of microstates available to the system, is quantified by the entropy. More possible different microstates means higher entropy.

The association with "disorder" is straightforward once "order" is properly defined, which, given the number of meanings attributed to the word, is not entirely trivial. From Merriam-Webster, this seems to fit the intended definition most closely when used in chemical circles :

a regular or harmonious arrangement

Regularity always implies lower entropy, all else being equal. It is therefore fair to associate "order" with lower entropy. This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system.

This is in answer to (primarily) the third question. The association with disorder is naturally anthropocentric, "disorder" is an idea based on our experience of the world, but it does synch with the concept of entropy as far as the statistical mechanical definition following Boltzmann $$S= k_\mathrm B \log \Omega$$ is concerned. $\Omega$, the number of microstates available to the system, is quantified by the entropy. More possible different microstates means higher entropy.

The association with "disorder" is straightforward once "order" is properly defined, which, given the number of meanings attributed to the word, is not entirely trivial. From Merriam-Webster, this seems to fit the intended definition most closely when used in chemical circles :

a regular or harmonious arrangement

Regularity always implies lower entropy, all else being equal. It is therefore fair to associate "order" with lower entropy. This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system.