Related papers: Computability of entropy and information in classi…
We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones.…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
We introduce and study several notions of computability-theoretic reducibility between subsets of $\omega$ that are "robust" in the sense that if only partial information is available about the oracle, then partial information can be…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
The information provided by a classical measurement is unambiguously determined by the mutual information between the output results and the measured quantity. However, quantum mechanically there are at least two notions of information…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last…
We investigate the capabilities of a quantum computer based on cold trapped ions in presence of non-dissipative decoherence. The latter is accounted by using the evolution time as a random variable and then averaging on a properly defined…
MaxEnt inference algorithm and information theory are relevant for the time evolution of macroscopic systems considered as problem of incomplete information. Two different MaxEnt approaches are introduced in this work, both applied to…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…