Look at the EPA sticker for the fridge, it should list kilowatt usage per day or per year. If it's per year, divide by 365 to get per day.
Taking the kw/day figure, divide by 12 to get the number of 12-volt amps the system will use in a day. Compare that figure to the amp-hour rating of the battery for the "dedicated system".
For example if the fridge is rated at 2 kw per day, 2000 / 12 is 166 amps per day (on a 12v system). Divide more to get amp-hours 166 / 24 = 7 amp-hours
Now lets say you have a modest battery system of 500 amp-hour total capacity. YOu can never use the total capacity, most folks use less than half, so 250 / 7 = 35 hours or a day and a half.
This is all rough math, there's a lot of variables that can change the numbers but for all intents, it's an accurate ball-park.
energy star for a 17 cu foot domestic