This looks like winter damage, perhaps a combination of typical winter burn on arborvitae and plants that weren't hydrated enough going into winter.
In the future, there are two important things to do going into winter. First is water, water, water, especially for young, newly planted evergreens in the fall. Second, for evergreens prone to winter burn, like arborvitae, consider wrapping them in burlap to prevent burning.
This past winter and spring have proven very hard on a number of trees and shrubs. We had warm weather last March and this caused many plants, including your arborvitae, to break their winter dormancy. The warming sun of March contributed to this. Your arborvitae were thus stimulated to begin photosynthesis. One of the requirements of photosynthesis is water. But then we had very cold temperatures in April. The ground refroze. Your arborvitae were unable to secure sufficient water. The browning that you are observing is essentially due to dehydration. Hence the suggestion of watering extremely well in the fall and using burlap to minimize direct heating by the sun.
The reality is that the brown branches will not recover. One option is to cut them back and, with time, remaining growth might cover up their absences though not completely. The other option, as hard it is to consider, is to replace these trees. The former may be a long-term possibility while the latter will be more immediate.
For whatever consolation it might be, your plight has been very common this season in Minnesota. Personally. I have lost three shrubs and perennials this season.
You may find the following to be of some interest.
Steve Thank you so much for the information. Your information has prompted another question. We planted a Fat Albert Blue Spruce this summer. We have been watering all summer, but will really water well this autumn. However should we plan on wrapping it in burlap as well?
In part the answer to your question depends on the location of the tree. If it is facing towards the south or south west, it will be most susceptible to winter burn. A burlap wrap might then be in order. Be sure to leave this wrap open at the top so your Fat Albert can "breathe". If the location is towards the north and in a protected spot, while wrapping could still be done it may not be necessary.