We present an operator formalism for the recently developed kinetic information theory, construct Poisson brackets between the Liouville and information 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.