Water and carbon are lost through perspiration and breathing.
How much mass is lost in this way in a single day for a typical person?
Biology Stack Exchange is a question and answer site for biology researchers, academics, and students. It only takes a minute to sign up.Sign up to join this community
The simplest route to your answer would be through the kcal consumed/expended equation.
1kg (2.2lbs) of fat has ~7700 kcal of energy. The average person requires roughly 2000kcal per day if they perform mild physical labor throughout their day - 25.9% of the total energy available in 1kg of fat. So you could say that if a person did not eat for a day they would lose ~1/4kg or 1/2lb of fat-mass.
I calculated the above in "fat" because it's the number I knew off-hand, but truth be told the amount of "mass" you'd lose also depends on density. Fat (9kcal/g) is more energy dense than alcohol (7kcal/g), carbohydrates/sugars (4kcal/g), and protein (4kcal/g). For the same energy expenditure of 2000kcal in a single day you would metabolise more than 1/2kg or 1lb of either carbohydrates or proteins.
In reality you will burn roughly equal amounts of fats and carbohydrates (assuming you're not forcing your body into a ketogenic state) at about a 55% fat/45% carbs ratio IIRC.
So, with the assumption that the person isn't on a keto diet, has sufficient fat reserves, and expends 2000kcal of energy in a single day while drinking enough water to replace what is used in the energy metabolism, you will lose ~.14kg of fat and ~.63kg of carbohydrates for a grand total of ~.77kg (~1.69lbs) of mass expended per day.
Since humans vary greatly, however, that is going to vary wildly. Personally speaking, it's easy for me to expend >3000kcal per day with an hour of moderate exercise since I'm simply bigger than the average person and require more energy to do anything. If you're shorter than average, do less work than average (i.e. - are sedentary), or hormonal conditions (which are rare and cannot be self-diagnosed) modify calorie expenditure, your numbers will be different.
Also worth it to note: Ghrelin, a major hunger-regulating hormone, changes its tonic behavior significantly if you go more than 2 days consuming less than 1200kcal. After 2 days fasting it will instigate changes that will result in more fat retained after you resume a regular eating schedule for up to 5 years... So starving yourself for a week to lose 5kg seems great until you realize you'll gain 10kg once you go back to a normal diet.
As always, if you're unsure of any diets please go to a qualified professional for consultation.