Computability of entropy and information in classical Hamiltonian systems

Details Computability of entropy and information in classical Hamiltonian systems Computability of entropy and information in classical Hamiltonian systems

2008-08-12

arxiv.org/abs/0808.1678v2

Physics Letters A 373 (2009), pp. 1409-1414

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.physleta.2009.02.050

We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a computable discrete partition. Using a recursively enumerable nonrecursive set it is shown that even though the initial probability distribution, entropy, Hamiltonian and its partial derivatives are computable under a computable partition, the time evolution of its information capacity under the original partition can grow faster than any recursive function. This implies that even though the probability measure and information are conserved in classical Hamiltonian time evolution we might not actually compute the information with respect to the original computable partition.

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