If you can get an aqueous solution of solids to completely crystallize (and sucrose does like to crystallize), it won't support microorganisms, but if it doesn't crystallize, it will have a critical "deliquescence relative humidity". When the relative humidity of the air is above the DRH†, the solution absorbs water from the air rather than giving up water to the air, and if there are crystals in it, they tend to shrink instead of growing.
Different solutes have different DRHs, but there are many of them whose affinity for water is so strong that their DRH is so low that under normal circumstances they never completely dry out. Some of them are commonly used as desiccants, such as lye, calcium chloride, and magnesium chloride. In general, mixing solutes tends to impede crystallization, so more heterogeneous mixtures like honey tend to have lower DRH than more homogeneous mixtures like pure sucrose.
(This is an engineering reason to add something like lemon juice when you make simple syrup: the citrate hydrolyzes some of the sucrose into glucose and fructose, greatly impeding crystallization and greatly improving your chances of having a pourable syrup when you want to use it next month.)
Under many circumstances, honey will eventually absorb enough water from the air by this mechanism to permit the growth of yeasts and bacteria. But it takes a remarkably long time.
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† The DRH does vary with temperature, but in most cases only slightly over the human-survivable range, so you can say "CaCl₂ has a DRH of about 40%" and be correct enough for many purposes.
Different solutes have different DRHs, but there are many of them whose affinity for water is so strong that their DRH is so low that under normal circumstances they never completely dry out. Some of them are commonly used as desiccants, such as lye, calcium chloride, and magnesium chloride. In general, mixing solutes tends to impede crystallization, so more heterogeneous mixtures like honey tend to have lower DRH than more homogeneous mixtures like pure sucrose.
(This is an engineering reason to add something like lemon juice when you make simple syrup: the citrate hydrolyzes some of the sucrose into glucose and fructose, greatly impeding crystallization and greatly improving your chances of having a pourable syrup when you want to use it next month.)
Under many circumstances, honey will eventually absorb enough water from the air by this mechanism to permit the growth of yeasts and bacteria. But it takes a remarkably long time.
______
† The DRH does vary with temperature, but in most cases only slightly over the human-survivable range, so you can say "CaCl₂ has a DRH of about 40%" and be correct enough for many purposes.