1. A computer system for relinquishing, by a selected processor, the selected processor's own exclusive ownership of a specified cache line, the computer system comprising: a selected private cache of a selected processor, the selected private cache configured to provide exclusive ownership of cache lines to the selected processor; and the selected processor configured to be a processor of a multi-processor system, each processor of the multi-processor system having a respective private cache, the computer system configured to perform a method comprising: executing, by the selected processor, a demote instruction of a software program, the demote instruction specifying an address of a specified cache line, the executing the demote instruction by the selected processor comprising: based on the computer system determining that the specified cache line in the selected private cache is exclusively owned by the selected processor, the executing the demote instruction, by the selected processor, causing the selected processor's exclusive ownership of the cache line in the selected private cache to be relinquished.