  Information-theoretic insights have proven fruitful in many areas of quantum
physics. But can the fundamental dynamics of quantum systems be derived from
purely information-theoretic principles, without resorting to Hilbert space
structures such as unitary evolution and self-adjoint observables? Here we
provide a model where the dynamics originates from a condition of informational
non-equilibrium, the deviation of the system's state from a reference state
associated to a field of identically prepared systems. Combining this idea with
three basic information-theoretic principles, we derive a notion of energy that
captures the main features of energy in quantum theory: it is observable,
bounded from below, invariant under time-evolution, in one-to-one
correspondence with the generator of the dynamics, and quantitatively related
to the speed of state changes. Our results provide an information-theoretic
reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions,
establishing a bridge between dynamical and information-theoretic notions.
