# Publications by PierGianLuca Porta Mana

## Toward a stochastic parameterization of ocean mesoscale eddies

OCEAN MODELLING **79** (2014) 1-20

## Notes on affine and convex spaces

(2011)

These notes are a short introduction to affine and convex spaces, written especially for physics students. They try to connect and summarize the different elementary presentations available in the mathematical literature. References are also provided, as well as an example showing the relevance and usefulness of affine spaces in classical physics.

## Conjectures and questions in convex geometry (of interest for quantum theory and other physical statistical theories)

(2011)

Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.

## On two recent conjectures in convex geometry

(2011)

Two conjectures recently proposed by one of the authors are disproved

## In favour of the time variable in classical thermoDYNAMICS

(2010)

A case for the teaching of classical thermodynamics with an explicit time variable, with phenomena involving changes in time, is made by presenting and solving a exercise in textbook style, and pointing out that a solution accords with experiment. The exercise requires an explicit treatment of the time variable. Further arguments are given for the advantages of an explicit time variable in classical thermodynamics, and against some standard terminology in this theory.

## On the relation between plausibility logic and the maximum-entropy principle: a numerical study

(2009)

What is the relationship between plausibility logic and the principle of maximum entropy? When does the principle give unreasonable or wrong results? When is it appropriate to use the rule `expectation = average'? Can plausibility logic give the same answers as the principle, and better answers if those of the principle are unreasonable? To try to answer these questions, this study offers a numerical collection of plausibility distributions given by the maximum-entropy principle and by plausibility logic for a set of fifteen simple problems: throwing dice.

## Effects of the g factor in semiclassical kinetic plasma theory

Physical Review Letters **101** (2008)

A kinetic theory for spin plasmas is put forward, generalizing those of previous authors. In the model, the ordinary phase space is extended to include the spin degrees of freedom. Together with Maxwell's equations, the system is shown to be energy conserving. Analyzing the linear properties, it is found that new types of wave-particle resonances are possible that depend directly on the anomalous magnetic moment of the electron. As a result, new wave modes, not present in the absence of spin, appear. The implications of our results are discussed. © 2008 The American Physical Society.

## `Plausibilities of plausibilities': an approach through circumstances

(2006)

Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a probability and that satisfies some additional logical properties. The idea, which can be traced to Laplace and Jaynes, is that the usual inferential reasonings about the probability-like parameters of a statistical model can be conceived as reasonings about equivalence classes of `circumstances' - viz., real or hypothetical pieces of knowledge, like e.g. physical hypotheses, that are useful in assigning a probability and satisfy some additional logical properties - that are uniquely indexed by the probability distributions they lead to.

## Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors

(2006)

This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in absolute frequencies of the outcomes of N identical von Neumann projective measurements performed on N identically prepared three-level systems. Various small values of N as well as the large-N limit are considered. Two kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; the other represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. In a companion paper the case of measurement data consisting in average values, and an additional prior studied by Slater, are considered.

## Consistency of the Shannon entropy in quantum experiments

Physical Review A - Atomic, Molecular, and Optical Physics **69** (2004)

The consistency of Shannon entropy applied to the statistical outcomes of quantum experiments was analyzed. The Shannon entropy was found to be fully consistent and its properties were not violated in quantum experiments. It was found that a change in the temporal order of the experiments led to change in entropy values of quantum experiments. It was observed that Shannon entropy is always context dependent in quantum experiments.

## A size criterion for macroscopic superposition states

Journal of Optics B: Quantum and Semiclassical Optics **6** (2004) 429-436

## Schrödinger-cat states - Size classification based on evolution or dissipation

Proceedings of SPIE - The International Society for Optical Engineering **5468** (2004) 335-343

The issue of estimating how "macroscopic" a superposition state is, can be addressed by analysing the rapidity of the state's evolution under a preferred observable, compared to that of the states forming the superposition. This fast evolution, which arises from the larger dispersion of the superposition state for the preferred operator, also represents a useful characteristic for interferometric applications. This approach can be compared to others in which a superposition's macroscopality is estimated in terms of the fragility to dissipation.

## Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary

Classical and Quantum Gravity **18** (2001) 779-792

A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d + 1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.

## The Laplace-Jaynes approach to induction

ArXiv (0)

An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that based on de Finetti's representation theorem and on the notion of infinite exchangeability. In particular, it gives an alternative interpretation of those formulae that apparently involve `unknown probabilities' or `propensities'. Various advantages and applications of the presented approach are discussed, especially in comparison to that based on exchangeability. Generalisations are also discussed.

## Why can states and measurement outcomes be represented as vectors?

ArXiv (0)

It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of these vectors are discussed, as well as some connexions with the quantum-mechanical formalism.

## On distinguishability, orthogonality, and violations of the second law: contradictory assumptions, contrasting pieces of knowledge

ArXiv (0)

Two statements by von Neumann and a thought-experiment by Peres prompts a discussion on the notions of one-shot distinguishability, orthogonality, semi-permeable diaphragm, and their thermodynamic implications. In the first part of the paper, these concepts are defined and discussed, and it is explained that one-shot distinguishability and orthogonality are contradictory assumptions, from which one cannot rigorously draw any conclusion, concerning e.g. violations of the second law of thermodynamics. In the second part, we analyse what happens when these contradictory assumptions comes, instead, from _two_ different observers, having different pieces of knowledge about a given physical situation, and using incompatible density matrices to describe it.

## Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior

ArXiv (0)

This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in the average of outcome values of N identical von Neumann projective measurements performed on N identically prepared three-level systems. In particular the large-N limit will be considered. Three kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; another one represented by a prior studied by Slater, which has been proposed as the natural measure on the set of statistical operators; the last prior is represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. The assigned statistical operators obtained with the first two kinds of priors are compared with the one obtained by Jaynes' maximum entropy method for the same measurement situation. In the companion paper the case of measurement data consisting in absolute frequencies is considered.