Paradox: Proof-of-work APPEARS to support the "labor theory of value".

Resolution: It isn't the work expended that we OBJECTIVELY value, it is the resultant state of order that we SUBJECTIVELY value.

Proof-of-Work (PoW) in Bitcoin is often characterized as a wasteful mechanism due to the energy it consumes. However, this energy consumption can be seen in a different light when viewed through the lens of thermodynamics. Taking the given statement into account: when miners perform PoW, they expend energy seeking a nonce that satisfies the network's current target difficulty. This energy expenditure predominantly transforms into heat. This heat production, as described, results in changes in the distribution of entropy of the system - essentially, heat dissipates, increasing the entropy in the surrounding environment.

Meanwhile, on the digital front, once the correct nonce is discovered, a block is validated and added to the blockchain, symbolizing a state of increased order, a negentropic process. Hence, in the PoW mechanism, entropy in the form of the unknown nonce is transferred to the environment as heat, while the digital realm gains order with the discovery and inscription of the nonce on the blockchain. This process metaphorically suggests that the inherent design of PoW moves entropy from the uncertain digital state (searching for the nonce) to the physical world, leaving behind increased order (validated blocks) in its wake.

PoW pulls entropy from the digital realm and disipates it in the physical.