89 research outputs found
Maximum-entropy theory of steady-state quantum transport
We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits
Conway games, algebraically and coalgebraically
Using coalgebraic methods, we extend Conway's theory of games to possibly
non-terminating, i.e. non-wellfounded games (hypergames). We take the view that
a play which goes on forever is a draw, and hence rather than focussing on
winning strategies, we focus on non-losing strategies. Hypergames are a
fruitful metaphor for non-terminating processes, Conway's sum being similar to
shuffling. We develop a theory of hypergames, which extends in a non-trivial
way Conway's theory; in particular, we generalize Conway's results on game
determinacy and characterization of strategies. Hypergames have a rather
interesting theory, already in the case of impartial hypergames, for which we
give a compositional semantics, in terms of a generalized Grundy-Sprague
function and a system of generalized Nim games. Equivalences and congruences on
games and hypergames are discussed. We indicate a number of intriguing
directions for future work. We briefly compare hypergames with other notions of
games used in computer science.Comment: 30 page
Some fundamental algebraic tools for the semantics of computation: Part 3. indexed categories
AbstractThis paper presents indexed categories which model uniformly defined families of categories, and suggests that they are a useful tool for the working computer scientist. An indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms. Similarly, an indexed functor (which is a uniform family of functors between the components categories) induces a flattened functor between the corresponding flattened categories. Under certain assumptions, flattened categories are (co)complete if all their components are, and flattened functors have left adjoints if all their components do. Several examples are given. Although this paper is Part 3 of the series “Some fundamental algebraic tools for the semantics of computation”, it is entirely independent of Parts 1 and 2
Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools
We provide simple equational principles for deriving rely-guarantee-style
inference rules and refinement laws based on idempotent semirings. We link the
algebraic layer with concrete models of programs based on languages and
execution traces. We have implemented the approach in Isabelle/HOL as a
lightweight concurrency verification tool that supports reasoning about the
control and data flow of concurrent programs with shared variables at different
levels of abstraction. This is illustrated on two simple verification examples
A Calculus of Space, Time, and Causality: its Algebra, Geometry, Logic
The calculus formalises human intuition and common sense about space, time, and causality in the natural world. Its intention is to assist in the design and implementation of programs, of programming languages, and of interworking by tool chains that support rational program development. The theses of this paper are that Concurrent Kleene Algebra (CKA) is the algebra of programming, that the diagrams of the Unified Modeling Language provide its geometry, and that Unifying Theories of Program- ming (UTP) provides its logic. These theses are illustrated by a fomalisation of features of the first concurrent object-oriented language, Simula 67. Each level of the calculus is a conservative extension of its predecessor. We conclude the paper with an extended section on future research directions for developing and applying UTP, CKA, and our calculus, and on how we propose to implement our algebra, geometry, and logic
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