What is the ~/.rnd file in openssl and how to generate a new private key with it?

The ~/.rnd file is owned by root if you've ever run a command that modifies ~/.rnd as root via sudo in its non-login mode (ie without -i). As for what the ~/.rnd file is, it contains a seed value for the OpenSSL random number generator. The least-worst docs I can find on it are the RAND_read_file(3) man page.