Vinegar (Acetic Acid) does not influence the metabolic rate. Nevertheless, one human study suggests that it may help with fat loss. Although it doesn't have the largest body of evidence, it remains a very cheap and safe 'home remedy' to aid in fat loss.
One study conducted had obese subjects consume either 0, 15, or 30mL vinegar (0, 750mg, 1,500mg Acetic Acid; respectively) in a double blind manner (placebo had added lactate to match taste). Weight loss was noted in a dose-dependent manner, and increased throughout the duration of the study. No differences in food intake were noted, and average weight loss appeared to be 1.0lbs in 12 weeks for the 15mL group and 2.0lbs in the 30mL group, with both groups regaining some weight 4 weeks after cessation. It was theorized that this was due to increased fat oxidation enzymes from AMPK.
This appears to be the only well controlled study done on vinegar and weight loss in humans, and it is currently not known whether taking vinegar in isolation or with a meal is more effective.
Vinegar appears to be effective at suppressing the speed at which glucose enters the blood, and with that lowers the peak glucose and insulin secretion. If measured acutely, there is a large (31.4%-40%) decrease in blood glucose levels, but after 120min the overall exposure is the same. It is a slowing effect, not a reducing effect. That being said, this slowing may be beneficial in improving insulin sensitivity in diabetics.
Vinegar does not seem to interfere with actual carbohydrate absorption in any way.
There have been reports of esophageal injury associated with apple cider vinegar tablets, although it is not sure if this is due to high acid concentration or due to product tampering.
It may be best to use regular table vinegar, as that will get the job done.
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