Abstract

We present an operator formalism for the recently developed kinetic information theory, construct Poisson brackets between the Liouville L and information Ĩ operators in μ space, proposing its quantum version. Making use of the universal quantum of time, the Planck time τp, a pseudo-energy-time uncertainty relation is constructed. It suggests that tiny amounts of information production may cause large variations in energy. The Hubble time τH sets an upper bound on information in the universe.

Highlights

  • In Treumann and Baumjohann [1] we have put forward the principles of a physical kinetic theory of information starting from the idea that information is based in the dynamics of many particle N ≫ 1 systems encountered in physics as well as in other domains of nature and society

  • HN the N-particle classical Hamiltonian. (In Equation 6 of that work a typo occurred: log IN should be replaced with log FN, and the sentence following it can be dropped.) We conjectured that it can be reduced by the methods of the BBGKY hierarchy construction to a one-particle N = 1 kinetic equation in Boltzmann’s 6-dimensional μ phase space

  • Preference for use of the total time derivative is justified by the equivalence to kinetic theory

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Summary

Introduction

In Treumann and Baumjohann [1] we have put forward the principles of a physical kinetic theory of information starting from the idea that information is based in the dynamics of many particle N ≫ 1 systems encountered in physics as well as in other domains of nature and society. The basic equation governing the N-particle (Boltzmann-Shannon-) information IN(FN) = FN log FN turned out to be the exact N-particle Liouville equation in Gibbs’ 6N-dimensional Ŵ phase space Its non-vanishing right-hand side C = 0, an information-production term, we related to the Kolmogorov [2] entropy rate C = K(I), with I ≡ I1.

Results
Conclusion

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