Agreeing to agree : contracts concerning marital rights (1993)

"10/1993.

Getting on with your life--what to do after the divorce is final (1993)

"10/1993.

Entropy, majorization and thermodynamics in general probabilistic theories

In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that every state has a decomposition, with unique probabilities, into perfectly distinguishable pure states. The spectral entropy, and analogues using other Schur-concave functions, can be defined as the entropy of these probabilities. We describe additional conditions under which the outcome probabilities of a fine-grained measurement are majorized by those for a spectral measurement, and therefore the "spectral entropy" is the measurement entropy (and therefore concave). These conditions are (1) projectivity, which abstracts aspects of the Lueders-von Neumann projection postulate in quantum theory, in particular that every face of the state space is the positive part of the image of a certain kind of projection operator called a filter; and (2) symmetry of transition probabilities. The conjunction of these, as shown earlier by Araki, is equivalent to a strong geometric property of the unnormalized state cone known as perfection: that there is an inner product according to which every face of the cone, including the cone itself, is self-dual. Using some assumptions about the thermodynamic cost of certain processes that are partially motivated by our postulates, especially projectivity, we extend von Neumann's argument that the thermodynamic entropy of a quantum system is its spectral entropy to generalized probabilistic systems satisfying spectrality.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Computational irreducibility and compatibilism: towards a formalization

If our actions are determined by the laws of nature, can we meaningfully claim to possess free will? Compatibilists argue that the answer is yes, and that free will is compatible with complete determinism. Previously, it has been suggested that the notion of computational irreducibility can shed light on this relation: it implies that there cannot in general be "shortcuts" to the decisions of agents, explaining why deterministic agents often appear to have free will. In this paper, we introduce a variant of computational irreducibility that intends to capture more accurately aspects of actual (as opposed to apparent) free will: computational sourcehood, i.e. the phenomenon that the successful prediction of a process' outputs must typically involve an almost-exact representation of the relevant features of that process, regardless of the time it takes to arrive at the prediction. We conjecture that many processes have this property, and we study different possibilities for how to formalize this conjecture in terms of universal Turing machines. While we are not able to settle the conjecture, we give several results and constructions that shed light on the quest for its correct formulation.Comment: 15 pages, 1 figur

Internal quantum reference frames for finite Abelian groups

Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained treatment of such quantum reference frames (QRFs) for the case when the underlying configuration space is a finite Abelian group, significantly extending our previous work (Quantum 5, 530 (2021)). The simplicity of this setup admits a fully rigorous quantum information-theoretic analysis, while maintaining sufficient structure for exploring many of the conceptual and structural questions also pertinent to more complicated setups. We exploit this to derive several important structures of constraint quantization with quantum information-theoretic methods and to reveal the relation between different approaches to QRF covariance. In particular, we characterize the "physical Hilbert space" -- the arena of the "perspective-neutral" approach -- as the maximal subspace that admits frame-independent descriptions of purifications of states. We then demonstrate the kinematical equivalence and, surprising, dynamical inequivalence of the "perspective-neutral" and the "alignability" approach to QRFs. While the former admits unitaries generating transitions between arbitrary subsystem relations, the latter, remarkably, admits no such dynamics when requiring symmetry-preservation. We illustrate these findings by example of interacting discrete particles, including how dynamics can be described "relative to one of the subsystems".Comment: 22 pages, 1 figure. V2: close to published versio

The HI content of Early-Type Galaxies from the ALFALFA survey I. Catalogued HI sources in the Virgo cluster

Aims: We are using the Arecibo Legacy Fast ALFA survey (ALFALFA), which is covering 17% of the sky at 21 cm, to study the HI content of Early-Type galaxies (ETG) in an unbiased way. The aim is to get an overall picture of the hot, warm and cold ISM of ETG, as a function of galaxy mass and environment, to understand its origin and fate, and to relate it to the formation and evolution history of these objects. Methods: This paper deals with the first part of our study, which is devoted to the 8-16 deg. declination strip in the Virgo cluster. In this sky region, using the Virgo Cluster Catalogue (VCC), we have defined an optical sample of 939 ETG, 457 of which are brighter than the VCC completeness limit at B_T=18.0. We have correlated this optical sample with the catalogue of detected HI sources from ALFALFA. Results: Out of the 389 ETG from the VCC with B_T<=18.0, outside the 1 deg. region of poor HI detection around M87, and corrected for background contamination of VCC galaxies without a known radial velocity, only 9 galaxies (2.3%) are detected in HI with a completeness limit of 3.5 and 7.6 x 10^7 Mo of HI for dwarf and giant ETG, respectively. In addition 4 VCC ETG with fainter magnitudes are also detected. Our HI detection rate is lower than previously claimed. The majority of the detected ETG appear to have peculiar morphology and to be located near the edges of the Virgo cluster. Conclusions: Our preliminary conclusion is that cluster ETG contain very little neutral gas, with the exceptions of a few peculiar dwarf galaxies at the edge of the ETG classification and of very few larger ETG, where the cold gas could have a recent external origin.Comment: Accepted for publication in Astronomy and Astrophysics; 6 pages, 3 figure