Are black holes about information?

Information theory is increasingly invoked by physicists concerned with fundamental physics, including black hole physics. But to what extent is the application of information theory in those contexts legitimate? Using the case of black hole thermodynamics and Bekenstein's celebrated argument for the entropy of black holes, I will argue that information-theoretic notions are problematic in the present case. Bekenstein's original argument, as suggestive as it may appear, thus fails. This example is particularly pertinent to the theme of the present collection because the Bekenstein-Hawking formula for black hole entropy is widely accepted as 'empirical data' in notoriously empirically deprived quantum gravity, even though the laws of black hole thermodynamics have so far evaded empirical confirmation.Comment: 20 pages; forthcoming in Richard Dawid, Radin Dardashti, and Karim Th\'ebault (eds.), Epistemology of Fundamental Physics, Cambridge University Press; minor changes and additions of reference

Mind the gap: transitions between concepts of information in varied domains

The concept of 'information' in five different realms – technological, physical, biological, social and philosophical – is briefly examined. The 'gaps' between these conceptions are discussed, and unifying frameworks of diverse nature, including those of Shannon/Wiener, Landauer, Stonier, Bates and Floridi, are examined. The value of attempting to bridge the gaps, while avoiding shallow analogies, is explained. With information physics gaining general acceptance, and biology gaining the status of an information science, it seems rational to look for links, relationships, analogies and even helpful metaphors between them and the library/information sciences. Prospects for doing so, involving concepts of complexity and emergence, are suggested

Thermodynamic analogies in economics and finance: instability of markets

Interest in thermodynamic analogies in economics is older than the idea of von Neumann to look for market entropy in liquidity, advice that was not taken in any thermodynamic analogy presented so far in the literature. In this paper we go further and use a standard strategy from trading theory to pinpoint why thermodynamic analogies necessarily fail to describe financial markets, in spite of the presence of liquidity as the underlying basis for market entropy. Market liquidity of frequently traded assets does play the role of the ‘heat bath‘, as anticipated by von Neumann, but we are able to identify the no-arbitrage condition geometrically as an assumption of translational and rotational invariance rather than (as finance theorists would claim) an equilibrium condition. We then use the empirical market distribution to introduce an asset’s entropy and discuss the underlying reason why real financial markets cannot behave thermodynamically: financial markets are unstable, they do not approach statistical equilibrium, nor are there any available topological invariants on which to base a purely formal statistical mechanics. After discussing financial markets, we finally generalize our result by proposing that the idea of Adam Smith’s Invisible Hand is a falsifiable proposition: we suggest how to test nonfinancial markets empirically for the stabilizing action of The Invisible Hand.Economics; utility; entropy and disorder; thermodynamics; financial markets; stochastic processes;

Thermodynamics for Trajectories of a Mass Point

On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated geometrically as dynamical variables. Statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamic variables are introduced through a partition function based on a canonical ensemble of trajectories. Within this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. The relationships between classical and quantum mechanics are discussed from this statistical mechanical viewpoint. The maximum entropy principle is shown to provide a unified view of both classical and quantum mechanics.Comment: 22 pages, 1 figur

Theory of Analogous Force on Number Sets

A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions p_{x} for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering p_{x} to describe complex phenomena, the theory leads to derive a distinct analogous force f_{x} on number sets proportional to $(\frac{\partial p_{x}}{\partial x} )_{T}$ at an analogous system temperature T. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.Comment: RevTeX, PostScript Fig, To Appear Phys.

Black Hole Thermodynamics: More Than an Analogy?

Black hole thermodynamics (BHT) is regarded as one of the deepest clues we have to a quantum theory of gravity. It motivates scores of proposals in the field, from the thought that the world is a hologram to calculations in string theory. The rationale for BHT playing this important role, and for much of BHT itself, originates in the analogy between black hole behavior and ordinary thermodynamic systems. Claiming the relationship is “more than a formal analogy,” black holes are said to be governed by deep thermodynamic principles: what causes your tea to come to room temperature is said additionally to cause the area of black holes to increase. Playing the role of philosophical gadfly, we pour a little cold water on the claim that BHT is more than a formal analogy. First, we show that BHT is often based on a kind of caricature of thermodynamics. Second, we point out an important ambiguity in what systems the analogy is supposed to govern, local or global ones. Finally, and perhaps worst, we point out that one of the primary motivations for the theory arises from a terribly controversial understanding of entropy. BHT may be a useful guide to future physics. Only time will tell. But the analogy is not nearly as good as is commonly supposed

Probability as a physical motive

Recent theoretical progress in nonequilibrium thermodynamics, linking the physical principle of Maximum Entropy Production ("MEP") to the information-theoretical "MaxEnt" principle of scientific inference, together with conjectures from theoretical physics that there may be no fundamental causal laws but only probabilities for physical processes, and from evolutionary theory that biological systems expand "the adjacent possible" as rapidly as possible, all lend credence to the proposition that probability should be recognized as a fundamental physical motive. It is further proposed that spatial order and temporal order are two aspects of the same thing, and that this is the essence of the second law of thermodynamics.Comment: Replaced at the request of the publisher. Minor corrections to references and to Equation 1 added