Related papers: Generalized Gibbs ensembles for time dependent pro…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
Most psychophysical experiments discard half the data collected. Specifically, experiments discard reaction time data, and use binary responses (e.g. yes/no) to measure performance. Here, Shannon's information theory is used to define…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
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…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
General relativity in the form where gravitational perturbations together with other physical fields propagate on an auxiliary background is considered. With using the Katz-Bi{\v{c}}\'ak-Lynden-Bell technique new conserved currents,…
We investigate how undecidability enters into computations of classical physical systems and contributes to the increase of entropy and loss of information. In actual computation with finite bit of information capacity we accept…
Using relative entropy, we derive bounds on the time rate of change of geometric entanglement entropy for any relativistic quantum field theory in any dimension. The bounds apply to both mixed and pure states, and may be extended to curved…
A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed…
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…
Whether the system under study is a shoal of fish, a collection of neurons, or a set of interacting atmospheric and oceanic processes, transfer entropy measures the flow of information between time series and can detect possible causal…
In this paper, we suppose a possible extension of Gibbs ensemble theory so that it can provide a reasonable description to phase transitions and spontaneous symmetry breaking. The extension is founded on three hypotheses, and can be…
In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…
Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the…
We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to…
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…
The statistical properties of physical systems in thermal equilibrium are blatantly different from their far-from-equilibrium counterparts. In the latter, fluctuations often dominate the dynamics and might cluster in ordered patterns in the…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…