In Infinispan Server 5.3 they are always enabled, with no way to disable them.
In Infinispan Server 6.0 they are enabled by default but there is a new statistics="true|false" attribute on <cache-container /> and <*-cache /> elements.
In Infinispan Server 7.0 they will be disabled by default for performance reasons.
Well, so, that's not what I want. I need to know when replication/distribution is done, how much time to be done and stuff like that. Is there a way to server.log show it?
Have you looked at the RpcManager MBean under each cache MBean. It provides stats such as averageReplicationTime, replicationCount, replicationFailures