EXORCIST XIV: The Wrath of Maxwell’s Demon. Part II. From Szilard to Landauer and Beyond

In this second part of our two-part paper we review and analyse attempts since 1950 to use information theoretic notions to exorcise Maxwell’s Demon. We argue through a simple dilemma that these attempted exorcisms are ineffective, whether they follow Szilard in seeking a compensating entropy cost in information acquisition or Landauer in seeking that cost in memory erasure. In so far as the Demon is a thermodynamic system already governed by the Second Law, no further supposition about information and entropy is needed to save the Second Law. In so far as the Demon fails to be such a system, no supposition about the entropy cost of information acquisition and processing can save the Second Law from the Demon.     

Reviving material theories of induction

John Norton says that philosophers have been led astray for thousands of years by their attempt to treat induction formally. He is correct that such an attempt has caused no end of trouble, but he is wrong about the history. There is a rich tradition of non-formal induction. In fact, material theories of induction prevailed all through antiquity and from the Renaissance to the mid-1800s. Recovering these past systems would not only fill lacunae in Norton’s own theory but would highlight areas where Norton has not freed himself from the straightjacket of formal induction as much as he might think. This essay begins that recovery.     

Against dogma: On superluminal propagation in classical electromagnetism

It is deeply entrenched dogma that relativity theory prohibits superluminal propagation. It is also experimentally well-established that under some circumstances, classical electromagnetic fields propagate through a dielectric medium with superluminal group velocities and superluminal phase velocities. But it is usually claimed that these superluminal velocities do not violate the relativistic prohibition. Here I analyze electromagnetic fields in a dielectric medium within a framework for understanding superluminal propagation recently developed by Geroch, 1996, Geroch, 2011 and elaborated by Earman (2014). I will argue that for some parameter values, electromagnetic fields do propagate superluminally in the Geroch–Earman sense.     

What are the drivers of induction? Towards a Material Theory+

John Norton's Material Theory of Induction (Norton, 2003, 2005, 2008, forthcoming) has a two-fold, negative and positive, goal. The negative goal is to establish that formal logics of induction fail if they are understood as universally applicable schemas of induction. The positive goal is to establish that it is material facts that enable and justify inductive inferences. I argue in this paper that Norton is more successful with his negative than with his positive ambition. While I do not deny that facts constitute an important type of enabler and justifier of inductions, they are by no means the only type. This paper suggests that there are no less than six other types of background information scientists need and use to fuel and warrant inductions. The discussion of additional enablers and justifiers of inductions will further show there are practically important and intellectually challenging methodological issues Norton's theory prevents us from seeing because it leaves out this or that type of enabler and justifier.     

States of ignorance and ignorance of states: Examining the Quantum Principal Principle

Earman (2018) has recently argued that the Principal Principle, a principle of rationality connecting objective chance and credence, is a theorem of quantum probability theory. This paper critiques Earman's argument, while also offering a positive proposal for how to understand the status of the Principal Principle in quantum probability theory.     

Spacetime structure

This paper makes an observation about the “amount of structure” that different classical and relativistic spacetimes posit. The observation substantiates a suggestion made by Earman (1989) and yields a cautionary remark concerning the scope and applicability of structural parsimony principles.     

Epistemic benefits of the material theory of induction

C. D. Broad famously labelled the problem of providing our inductive practices with a proper justification “the scandal of philosophy” (Broad, 1952). Recently, John Norton has provided a dissolution of this problem (2014). According to Norton, inductive inference is grounded in particular facts obtaining within particular domains (J. Norton, 2003b, 2010, 2014). Because the material theory does not involve a universal schema of induction, Norton claims it dissolves the problem of induction (which implies that such universal schemas cannot be justified).In this paper, I critically evaluate Norton's dissolution. In particular, I argue that the problem of induction is an epistemological problem, that Norton's material theory entails an externalist epistemology, and that it is a common feature of such epistemologies that they dissolve the problem of induction. The upshot is that the material theory is not unique in its ability to reap the specifically epistemic benefits of dissolving the problem of induction, and thus that the epistemic advantages of the material theory over extant alternatives in this regard are fewer than it may appear at first sight.     

Non-integrability and mixing in quantum systems: On the way to quantum chaos

In spite of the increasing attention that quantum chaos has received from physicists in recent times, when the subject is considered from a conceptual viewpoint the usual opinion is that there is some kind of conflict between quantum mechanics and chaos. In this paper we follow the program of Belot and Earman, who propose to analyze the problem of quantum chaos as a particular case of the classical limit of quantum mechanics. In particular, we address the problem on the basis of our account of the classical limit, which in turn is grounded on the self-induced approach to decoherence. This strategy allows us to identify the conditions that a quantum system must satisfy to lead to non-integrability and to mixing in the classical limit.     

Waiting for Landauer

Landauer's Principle asserts that there is an unavoidable cost in thermodynamic entropy creation when data is erased. It is usually derived from incorrect assumptions, most notably, that erasure must compress the phase space of a memory device or that thermodynamic entropy arises from the probabilistic uncertainty of random data. Recent work seeks to prove Landauer's Principle without using these assumptions. I show that the processes assumed in the proof, and in the thermodynamics of computation more generally, can be combined to produce devices that both violate the second law and erase data without entropy cost, indicating an inconsistency in the theoretical system. Worse, the standard repertoire of processes selectively neglects thermal fluctuations. Concrete proposals for how we might measure dissipationlessly and expand single molecule gases reversibly are shown to be fatally disrupted by fluctuations. Reversible, isothermal processes on molecular scales are shown to be disrupted by fluctuations that can only be overcome by introducing entropy creating, dissipative processes.     

Can we know the global structure of spacetime?

Here, we briefly review the notion of observational indistinguishability within the context of classical general relativity. We settle a conjecture given by Malament [(1977). Observationally indistinguishable space-times. In J. Earman, C. Glymour, & J. Statchel (Eds.), Foundations of space–time theories. Minnesota studies in the philosophy of science (Vol. VIII, pp. 61–80). Minneapolis: University of Minnesota Press] concerning the subject and then strengthen the result considerably. The upshot is this: There seems to be a robust sense in which the global structure of every cosmological model is underdetermined.     

Combining Economic Forecasts by Using a Maximum Entropy Econometric Approach

This paper explores the use of a maximum entropy econometric approach to combine forecasts when the small amount of information available does not allow the use of regression procedures since a dimensionality problem arises. This approach has its roots in information theory and builds on the entropy information measures and the classical maximum entropy principle, which was developed to recover information from underdetermined models. More specifically, we use the maximum entropy econometric approach for the measure of Shannon and we also propose its extension to the quadratic uncertainty measure. The experimental results over a pool of forecasts referring to Spanish inflation show some improvements when compared with equally weighted combined forecasting. Copyright © 2011 John Wiley & Sons, Ltd.     

Trust in expert testimony: Eddington's 1919 eclipse expedition and the British response to general relativity

The 1919 British astronomical expedition led by Arthur Stanley Eddington to observe the deflection of starlight by the sun, as predicted by Einstein's relativistic theory of gravitation, is a fascinating example of the importance of expert testimony in the social transmission of scientific knowledge. While Popper lauded the expedition as science at its best, accounts by Earman and Glymour, Collins and Pinch, and Waller are more critical of Eddington's work. Here I revisit the eclipse expedition to dispute the characterization of the British response to general relativity as the blind acceptance of a partisan's pro-relativity claims by colleagues incapable of criticism. Many factors served to make Eddington the trusted British expert on relativity in 1919, and his experimental results rested on debatable choices of data analysis, choices criticized widely since but apparently not widely by his British contemporaries. By attending to how and to whom Eddington presented his testimony and how and by whom this testimony was received, I suggest, we may recognize as evidentially significant corroborating testimony from those who were expert not in relativity but in observational astronomy. We are reminded that even extraordinary expert testimony is neither offered nor accepted entirely in an epistemic vacuum.     

Quantum sidelights on The Material Theory of Induction

John Norton's The Material Theory of Induction bristles with fresh insights and provocative ideas that provide a much needed stimulus to a stodgy if not moribund field. I use quantum mechanics (QM) as a medium for exploring some of these ideas. First, I note that QM offers more predictability than Newtonian mechanics for the Norton dome and other cases where classical determinism falters. But this ability of QM to partially cure the ills of classical determinism depends on facts about the quantum Hamiltonian operator that vary from case to case, providing an illustration of Norton's theme of the importance of contingent facts for inductive reasoning. Second, I agree with Norton that Bayesianism as developed for classical probability theory does not constitute a universal inference machine, and I use QM to explain the sense in which this is so. But at the same time I defend a brand of quantum Bayesianism as providing an illuminating account of how physicists' reasoning about quantum events. Third, I argue that if the probabilities induced by quantum states are regarded as objective chances then there are strong reasons to think that fair infinite lotteries are impossible in a quantum world.     

Theories of Newtonian gravity and empirical indistinguishability

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a “weak” version and a “strong” version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a “weak” version in Maxwellian spacetime, and a “strong” version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism.     

Can the maximum entropy principle be explained as a consistency requirement?

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Rényi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions.     

The use of the information-theoretic entropy in thermodynamics

When considering controversial thermodynamic scenarios such as Maxwell's demon, it is often necessary to consider probabilistic mixtures of macrostates. This raises the question of how, if at all, to assign entropy to them. The information-theoretic entropy is often used in such cases; however, no general proof of the soundness of doing so has been given, and indeed some arguments against doing so have been presented. We offer a general proof of the applicability of the information-theoretic entropy to probabilistic mixtures of macrostates that is based upon a probabilistic generalisation of the Kelvin statement of the second law. We defend the latter and make clear the other assumptions on which our main result depends. We also briefly discuss the interpretation of our result.     

台风形成库区降雨的影响因子挖掘

考虑影响台风降雨因素的复杂性以及现有水库台风遥测资料的不完备性,采用基于信息熵与条件信息熵建立起来的不完备信息系统的约简方法,对台风形成库区降雨的影响因子进行挖掘.以典型水库中的台风特性参数及库区降雨实时监测信息为依据,忽略环境因素影响,重点研究包括台风风速、风力、7级/10级风圈半径、中心气压、台风中心与库区距离等典型台风特性因子对库区降雨量的影响,经信息约简认为台风风速、中心气压、与库区距离等台风特性因子是库区降雨的主要影响因子.分析结果对水库台风监测及库区降雨强度分析具有一定指导作用.     

State of the field: Measuring information and confirmation

The aim of this paper is to survey and discuss some key connections between information and confirmation within a broadly Bayesian framework. We mean to show that treating information and confirmation in a unified fashion is an intuitive and fruitful approach, fostering insights and prospects in the analysis of a variety of related notions such as belief change, partial entailment, entropy, the value of experiments, and more besides. To this end, we recapitulate established theoretical achievements, disclose a number of underlying links, and provide a few novel results.     

The Limits of Information

Black holes have their own thermodynamics including notions of entropy and temperature and versions of the three laws. After a light introduction to black hole physics, I recollect how black hole thermodynamics evolved in the 1970s, while at the same time stressing conceptual points which were given little thought at that time, such as why the entropy should be linear in the black hole's surface area. I also review a variety of attempts made over the years to provide a statistical mechanics for black hole thermodynamics. Finally, I discuss the origin of the information bounds for ordinary systems that have arisen as applications of black hole thermodynamics.