ALGORITHMIC RANDOMNESS, PHYSICAL ENTROPY, MEASUREMENTS, AND THE SECOND LAW
Wojciech Hubert Zurek · WORLD SCIENTIFIC eBooks · 1992
Algorithmic information content is equal to the size -- in the number of bits -- of the shortest program for a universal Turing machine which can reproduce a state of a physical system. In contrast to the statistical Boltzmann-Gibbs-Shannon entropy, which measures ignorance, the algorithmic information content is a measure of the available information. It is defined without a recourse to probabilities and can be regarded as a measure of randomness of a definite microstate. I suggest that the physical entropy S -- that is, the quantity which determines the amount of the work {Delta}W which can be extracted in the cyclic isothermal expansion process through the equation {Delta}W = k{sub B}T{Delta}S -- is a sum of two contributions: the mission information measured by the usual statistical entropy and the known randomness measured by the algorithmic information content. The sum of these two contributions is a constant of motion'' in the process of a dissipation less measurement on an equilibrium ensemble. This conservation under a measurement, which can be traced back to the noiseless coding theorem of Shannon, is necessary to rule out existence of a successful Maxwell's demon. 17 refs., 3 figs.