People tend to distribute information evenly in language production for better and clearer communication. In this study, we compared essays written by second language learners with various native language (L1) backgrounds to investigate how they distribute information in their non-native language (L2) production. Analyses of surprisal and constancy of entropy rate indicated that writers with higher L2 proficiency can reduce the expected uncertainty of language production while still conveying informative content. However, the uniformity of information distribution showed less variability among different groups of L2 speakers, suggesting that this feature may be universal in L2 essay writing and less affected by L2 writers' variability in L1 background and L2 proficiency.