Security on the network depends on the hash rate. If one theoretically had unlimited energy, then it would basically be fiat energy at that point. Part of the security comes from the fact that it would take a great deal of both energy and computing power to attack the network.

If there was theoretically unlimited energy available to bad actors, I'm trying to decide if that would be a problem. If it doesn't cost anything other than [free] computational power to mine blocks, what would that mean for the network?

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Energy could approach $0, but the ASICs will still be a substantial cost. Also these costs would be available to both honest and dishonest actors; game theory says it will be orders of magnitude more profitable to mine BTC than to attempt to attack and destroy it.