Giovanni Valente

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian equilibrium values agree with Gibbsian phase averages. In this paper, we analyse their argument, which is still important today, and point out that its scope is limited to dilute gases.

This paper discusses the outstanding problem of replicability of empirical data in the context of recent work on meta-analysis, especially within the field of evidence-based medicine. Specifically, it deals with the methodological issue of how to determine the degrees of heterogeneity between different collected studies. After critically reviewing the standard measures used to quantify meta-analytical heterogeneity, we argue that they should be revised in such a way to take into account the statistical power of the individual studies. We thus propose some new measures of heterogeneity. Subsequently, we apply them to re-assess concrete case-studies from clinical research, thereby showing explicitly how the relevant values of heterogeneity diverge from those obtained with the original measures.

In recent years, the biomedical field has witnessed the emergence of novel tools and modelling techniques driven by the rise of the so-called Big Data. In this paper, we address the issue of predictability in biomedical Big Data models of cancer patients, with the aim of determining the extent to which computationally driven predictions can be implemented by medical doctors in their clinical practice. We show that for a specific class of approaches, called k-Nearest Neighbour algorithms, the ability to draw predictive inferences relies on a geometrical, or topological, notion of similarity encoded in a well-defined metric, which determines how close the characteristics of distinct patients are on average. We then discuss the conditions under which the relevant models can yield reliable and trustworthy predictive outcomes.

In this paper we aim to develop an indispensability argument in support of the existence of virtual particles in scattering processes. In order to avoid the Paradox of Infinite Limits, which allegedly poses a challenge to scientific realism, one needs to de-idealize the fictitious systems introduced by the two limiting procedures employed in the perturbation scheme, namely the infinite expansion in Dyson series and the limits for negative and positive infinite times associated with the assumption of free particles. We show that these limits do not introduce essential idealizations, in agreement with scientific realism. What is more, according to our argument, unobservable virtual particles arise as essential approximations and they should be interpreted as propagators of the interaction responsible for subatomic scattering. As such, their existence is based on the use of approximations that matter.

This chapter distinguishes between different uses of mathematical limits in physics and determines the conditions under which an infinite limit should be understood as giving rise to an “infinite idealization,” intended as a misrepresentation of the target system by way of introducing an infinite system. It points out that when infinite limits are used as infinite idealizations they can lead one to the Paradox of Infinite Limits, which allegedly poses a threat to scientific realism. In particular, this depends on whether the idealization is _essential_ for the explanation of the physical phenomenon under investigation. Instead, other uses of infinite limits such as approximations and abstractions do not raise any substantial problem for scientific realism. The chapter also argues that, even in the case of “essential idealizations,” there are ways of coping with the alleged incompatibility between infinite idealizations and scientific realism, which ultimately rely on empirical considerations.

This article provides an epistemological assessment of climate analogue methods, with specific reference to the use of spatial analogues in the study of the future climate of target locations. Our contention is that, due to formal and conceptual inadequacies of geometrical dissimilarity metrics and the loss of relevant information, especially when reasoning from the physical to the socio-economical level, purported inferences from climate analogues of the spatial kind we consider here prove limited in a number of ways. Indeed, we formulate five outstanding problems concerning the search for best analogues, which we call the problem of non-uniqueness of the source, problem of non-uniqueness of the target, problem of average, problem of non-causal correlations and problem of inferred properties, respectively. In the face of such problems, we then offer two positive recommendations for a fruitful application of this methodology to the assessment of impact, adaptation and vulnerability studies of climate change, especially in the context of what we may prosaically dub “twin cities”. Arguably, such recommendations help decision-makers constrain the set of plausible climate analogues by integrating local knowledge relevant to the locations of interest.

This paper addresses the role of analogical reasoning in archaeoastronomy - the discipline which studies the connections between the ancient monuments and the heavens. Archaeoastronomy is a highly interdisciplinary science, placed at the border between the humanities – especially archaeology – and the scientific approach to cultural heritage. As a consequence, its scientific foundations are a delicate matter. We plan to investigate here the question of what constitutes the evidence for analogical inferences in archaeoastronomy and to what extent one can achieve confirmation of archaeoastronomical hypotheses by means of such analogies. Our claim will be that, when deployed in accordance with the methodology articulated in this paper, analogies can be a highly effective epistemic tool for generating and supporting hypotheses about the relation of archaeological sites with astronomical events.

Integrated assessment models play a major role in the science and policy of climate change. Similarly to other widely used computational tools for addressing socially relevant problems, IAMs need to account for the key uncertainties characterizing processes and socio-economic responses. In the case of climate change, these are particularly complex given the very long-term nature of climate and the deep uncertainty characterizing technological and human systems. Here we draw from philosophical discussion of mathematical modeling of social problems and review the role of uncertainty in climate-economic modeling. In agreement with the literature, we highlight the crucial role of epistemic uncertainty in IAMs. We posit that the normative components of models, more than the physical and socio-techno-economic ones, are the most fraught by uncertainty and yet the least understood. We suggest a research agenda to explore uncertainties of evaluation frameworks, transcending the current implicit normativity of IAMs.

Econophysics is a branch of economics that applies concepts and methods from physics to the financial markets. This article focuses on the approaches to quantum finance developed by Kirill Ilinski and Belal E. Baaquie to deal with the uncertainty characterizing financial time series. Allegedly, their models rest on a formal analogy between quantum mechanics and finance. In order to evaluate them, we raise the question what is really quantum in quantum econophysics. We then argue that the supposed analogy breaks in an important manner, which is relevant to explain the empirical success of the proposed models.

Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The study of the evolution of superoscillations as initial datum of field equations requires the notion of supershift, which generalizes the concept of superoscillations. The present paper has a dual purpose. The first one is to give an updated and self-contained explanation of the strategy to study the evolution of superoscillations by referring to the quantum-mechanical Schrödinger equation and its variations. The second purpose is to treat the Dirac equation in relativistic quantum theory. The treatment of the evolution of superoscillations for the Dirac equation can be deduced by recent results on the Klein–Gordon equation, but further additional considerations are in order, which are fully described in this paper.

This paper discusses an outstanding issue in philosophy of physics concerning the relation between quantum symmetries and the notion of physical equivalence. Specifically, it deals with a dilemma arising for quantum symmetry breaking that was posed by Baker, who claimed that if two ground states are connected by a symmetry, even when it is broken, they must be physically equivalent. However, I argue that the dilemma is just apparent. In fact, I object to Baker’s conclusion by showing that the two thermodynamical phases of a ferromagnet, which are connected by the so-called flip-flop symmetry, are physically inequivalent, thereby providing a counter-example to his claim.

This paper discusses an argument by Norton to the effect that reversible processes in thermodynamics have paradoxical character, due to the infinite-time limit. For Norton, one can “dispel the fog of paradox” by adopting a distinction between idealizations and approximations, which he himself puts forward. Accordingly, reversible processes ought to be regarded as approximations, rather than idealizations. Here, we critically assess his proposal. In doing so, we offer a resolution of his alleged paradox based on the original work by Tatiana Ehrenfest-Afanassjeva on the foundations of thermodynamics.

This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory . In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events

This paper discusses a claim by Clifton and Halvorson (2001) that, contrary to non-relativistic quantum mechanics, local operations can never destroy entanglement in relativistic quantum field theory. The impossibility of achieving local disentanglement would raise a threat for the mutual independence between microscopic subsystems. Here, we observe that Clifton and Halvorson no-go result rests on an unnecessarily strong notion of local operations, which we label absolutely local operations, and we argue that a weaker notion, namely that of relatively local operations, is sufficient to guarantee that acting on one subsystem does not have non-local effects on another spacelike separated subsystem. We then show that one can achieve local disentanglement in relativistic quantum field theory by means of relatively local operations. In fact, we prove that, under the split property, there exists a class of disentangling relatively local operations.

Since the 1909 work of Carathéodory, formulations of thermodynamics have gained ground which highlight the role of the the binary relation of adiabatic accessibility between equilibrium states. A feature of Carathéodory's system is that the version therein of the second law contains an ambiguity about the nature of irreversible adiabatic processes, making it weaker than the traditional Kelvin-Planck statement of the law. This paper attempts first to clarify the nature of this ambiguity, by defining the arrow of time in thermodynamics by way of the Equilibrium Principle. It then argues that the ambiguity reappears in the important 1999 axiomatisation due to Lieb and Yngvason.

This paper develops a philosophical investigation of the merits and faults of a theorem by Lanford , Lanford , Lanford for the problem of the approach towards equilibrium in statistical mechanics. Lanford’s result shows that, under precise initial conditions, the Boltzmann equation can be rigorously derived from the Hamiltonian equations of motion for a hard spheres gas in the Boltzmann-Grad limit, thereby proving the existence of a unique solution of the Boltzmann equation, at least for a very short amount of time. We argue that, by establishing a statistical H-theorem, it offers a prospect to complete Boltzmann’s combinatorial argument, without running against the objections which plug other typicality-based approaches. However, we submit that, while recovering the irreversible approach towards equilibrium for positive times, it fails to predict a monotonic increase of entropy for negative times, and hence it yields the wrong retrodictions about the past evolution of a gas

It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford’s theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all

This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present the reasons why his axiomatic program remained an “unsolved problem” in mathematical physics. A recent unpublished result by Huzimiro Araki, proving that no algebra with a tracial state defined on it, such as the type II1II1 factors, can support any (regular) representation of the canonical commutation relations, is also reviewed and its consequences for von Neumann's projects are discussed.

This article investigates the nature of entangled correlations in algebraic quantum field theory (AQFT). We define a notion of local disentanglement, expressing the possibility of destroying entanglement by means of local operations. Contrary to the case of ordinary quantum mechanics, local disentanglement cannot be achieved in general in relativistic quantum field theory. However, we show that if the split property holds, there exists a local operation that can destroy entanglement between spacelike-separated quantum field systems.