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- W4289601539 abstract "We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be stated as follows: if we evolve the dynamical system for $n$ time steps and then we disturb it, it is the same as first disturbing the system with the same influence and then letting the system evolve for $n$ time steps. Applying the powerful machinery of resource theories, we develop a theory of covariant influences both when there is a purely deterministic evolution and when randomness is involved. Subsequently, we provide necessary and sufficient conditions for the transition between states under deterministic covariant influences and necessary conditions in the presence of stochastic covariant influences, predicting which transitions between states are forbidden. Our approach, for the first time, employs the framework of resource theories, borrowed from quantum information theory, to the study of finite discrete dynamical systems. The laws we articulate unify the behaviour of different types of finite discrete dynamical systems, and their mathematical flavour makes them rigorous and checkable." @default.
- W4289601539 created "2022-08-03" @default.
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- W4289601539 date "2021-11-26" @default.
- W4289601539 modified "2023-09-29" @default.
- W4289601539 title "Covariant influences for finite discrete dynamical systems" @default.
- W4289601539 doi "https://doi.org/10.48550/arxiv.2111.13695" @default.
- W4289601539 hasPublicationYear "2021" @default.
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