Jaynes’ information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution p of the underlying microscopic phase space trajectories over a time interval of length τ satisfies p ∝ exp(τσ /2kB) where σ is the time-averaged rate of entropy production of . Three consequences of this result ...

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon’s entropy function has a complementary dual function which we call “extropy.” The entropy and the extropy of a binary distribution are identical. However, the measure bifurcates into a pair of d...

In this paper the perturbation theory with the frequency of transition in atom as perturbation parameter is constructed. The estimation of the reminder term of series of this perturbation theory is given. With the help of this perturbation theory we have found an exact asymptotics of eigenvalues of complete hamiltonian in the limit of high quantum numbers. It is shown that the counter-rotating ...

Entanglement is a defining feature of quantum mechanics that makes fundamental distinctions between quantum and classical physics. As an unambiguous and quantifiable property of sufficiently simple multi-party quantum systems, entanglement has a definite time evolution that has recently begun to be studied in several contexts [1, 2, 3, 4, 5, 6, 7, 8]. Entanglement in a quantum system may deteri...

Title of dissertation: THERMODYNAMICS, REVERSIBILTY AND JAYNES’ APPROACH TO STATISTICAL MECHANICS Daniel N. Parker, Doctor of Philosophy, 2006 Dissertation directed by: Professor Jeffrey Bub Department of Philosophy This dissertation contests David Albert’s recent arguments that the proposition that the universe began in a particularly low entropy state (the “past hypothesis”) is necessary and ...

Tile Sumerian proverb in the title is invoked by Julian Jaynes (1976) as he documents the laborious process of coming to consciousness. This activity is the cognitive labor that enables us to arrive at a question about the precise relationship between two types of knowledge, or ask if "rhetorical relations [are] the realizations of intentions, or should . . . be discarded as simply a misconstru...

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian “Occam’s Razor”. This is illustrated with a simple example involving what Jaynes called a “sure thing” hypothesis. Jaynes’ resolution o...

The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To analyse the dynamical evolution of the atom-radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alter...

The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the...

ICA deals with finding linear projections in the input space along which the data shows most independence. Therefore, mutual information between the projected outputs, which are usually called the separated outputs due to links with blind source separation (BSS), is considered to be a natural criterion for ICA. Minimization of the mutual information requires primarily the estimation of this qua...