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If not SPV mining, so-called "empty blocks" occur if there are no available transactions to include and is usually when the previous block was solved a short period of time previously.
Is there any reason for this to happen more often if the previous block was solved by the same entity?
It is actually less likely to occur by the same miner. The reason for this is the fact that the miner that found the Block will have already validated it, thus it knows which transactions from the mempool were used. If the block is mined by another person their mining software might not have validated the previously mined block yet, which causes them to be unaware of which transactions were included. Thus an empty block is more likely when it was mined by someone else.
No, succeeding blocks by the same entity should never be empty.
Empty blocks occur when another miner finds a block before they have validated the previous block. Before having validated the previous block they don't know which transactions remain unconfirmed. However, if they'd include a transaction that was already confirmed their block would be invalid. Thus, to play it safe, they restart mining on an empty block.
As the miner that created the last block knows exactly which transactions where included from the start, they have no reason to mine empty block and can immediately include transactions.
