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Policies significantly shape computation's societal impact, a crucial HCI concern. However, challenges persist when HCI professionals attempt to integrate policy into their work or affect policy outcomes. Prior research considered these challenges at the ``border'' of HCI and policy. This paper asks: What if HCI considers policy integral to its intellectual concerns, placing system-people-policy interaction not at the border but nearer the center of HCI research, practice, and education? What if HCI fosters a mosaic of methods and knowledge contributions that blend system, human, and policy expertise in various ways, just like HCI has done with blending system and human expertise? We present this re-imagined HCI-policy relationship as a provocation and highlight its usefulness: It spotlights previously overlooked system-people-policy interaction work in HCI. It unveils new opportunities for HCI's futuring, empirical, and design projects. It allows HCI to coordinate its diverse policy engagements, enhancing its collective impact on policy outcomes., Comment: Proceedings of the 2024 CHI Conference on Human Factors in Computing Systems (CHI '24)

Reinforcement learning from human feedback (RLHF) has emerged as a powerful technique to make large language models (LLMs) easier to use and more effective. A core piece of the RLHF process is the training and utilization of a model of human preferences that acts as a reward function for optimization. This approach, which operates at the intersection of many stakeholders and academic disciplines, remains poorly understood. RLHF reward models are often cited as being central to achieving performance, yet very few descriptors of capabilities, evaluations, training methods, or open-source models exist. Given this lack of information, further study and transparency is needed for learned RLHF reward models. In this paper, we illustrate the complex history of optimizing preferences, and articulate lines of inquiry to understand the sociotechnical context of reward models. In particular, we highlight the ontological differences between costs, rewards, and preferences at stake in RLHF's foundations, related methodological tensions, and possible research directions to improve general understanding of how reward models function., Comment: 13 pages, 1 figure

Reinforcement learning from human feedback (RLHF) is a technique for training AI systems to align with human goals. RLHF has emerged as the central method used to finetune state-of-the-art large language models (LLMs). Despite this popularity, there has been relatively little public work systematizing its flaws. In this paper, we (1) survey open problems and fundamental limitations of RLHF and related methods; (2) overview techniques to understand, improve, and complement RLHF in practice; and (3) propose auditing and disclosure standards to improve societal oversight of RLHF systems. Our work emphasizes the limitations of RLHF and highlights the importance of a multi-faceted approach to the development of safer AI systems.

As AI technology advances rapidly, concerns over the risks of bigness in digital markets are also growing. The EU's Digital Markets Act (DMA) aims to address these risks. Still, the current framework may not adequately cover generative AI systems that could become gateways for AI-based services. This paper argues for integrating certain AI software as core platform services and classifying certain developers as gatekeepers under the DMA. We also propose an assessment of gatekeeper obligations to ensure they cover generative AI services. As the EU considers generative AI-specific rules and possible DMA amendments, this paper provides insights towards diversity and openness in generative AI services., Comment: ICML'23 Workshop Generative AI + Law (GenLaw)

Attention capitalism has generated design processes and product development decisions that prioritize platform growth over all other considerations. To the extent limits have been placed on these incentives, interventions have primarily taken the form of content moderation. While moderation is important for what we call "acute harms," societal-scale harms -- such as negative effects on mental health and social trust -- require new forms of institutional transparency and scientific investigation, which we group under the term accountability infrastructure. This is not a new problem. In fact, there are many conceptual lessons and implementation approaches for accountability infrastructure within the history of public health. After reviewing these insights, we reinterpret the societal harms generated by technology platforms through reference to public health. To that end, we present a novel mechanism design framework and practical measurement methods for that framework. The proposed approach is iterative and built into the product design process, and is applicable for both internally-motivated (i.e. self regulation by companies) and externally-motivated (i.e. government regulation) interventions for a range of societal problems, including mental health. We aim to help shape a research agenda of principles for the design of mechanisms around problem areas on which there is broad consensus and a firm base of support. We offer constructive examples and discussion of potential implementation methods related to these topics, as well as several new data illustrations for potential effects of exposure to online content., Comment: 63 pages, 5 tables and 6 figures

Optimization is offered as an objective approach to resolving complex, real-world decisions involving uncertainty and conflicting interests. It drives business strategies as well as public policies and, increasingly, lies at the heart of sophisticated machine learning systems. A paradigm used to approach potentially high-stakes decisions, optimization relies on abstracting the real world to a set of decision(s), objective(s) and constraint(s). Drawing from the modeling process and a range of actual cases, this paper describes the normative choices and assumptions that are necessarily part of using optimization. It then identifies six emergent problems that may be neglected: 1) Misspecified values can yield optimizations that omit certain imperatives altogether or incorporate them incorrectly as a constraint or as part of the objective, 2) Problematic decision boundaries can lead to faulty modularity assumptions and feedback loops, 3) Failing to account for multiple agents' divergent goals and decisions can lead to policies that serve only certain narrow interests, 4) Mislabeling and mismeasurement can introduce bias and imprecision, 5) Faulty use of relaxation and approximation methods, unaccompanied by formal characterizations and guarantees, can severely impede applicability, and 6) Treating optimization as a justification for action, without specifying the necessary contextual information, can lead to ethically dubious or faulty decisions. Suggestions are given to further understand and curb the harms that can arise when optimization is used wrongfully., Comment: 14 pages, 1 figure, presentation at FAccT23

AI documentation is a rapidly-growing channel for coordinating the design of AI technologies with policies for transparency and accessibility. Calls to standardize and enact documentation of algorithmic harms and impacts are now commonplace. However, documentation standards for AI remain inchoate, and fail to match the capabilities and social effects of increasingly impactful architectures such as Large Language Models (LLMs). In this paper, we show the limits of present documentation protocols, and argue for dynamic documentation as a new paradigm for understanding and evaluating AI systems. We first review canonical approaches to system documentation outside the context of AI, focusing on the complex history of Environmental Impact Statements (EISs). We next compare critical elements of the EIS framework to present challenges with algorithmic documentation, which have inherited the limitations of EISs without incorporating their strengths. These challenges are specifically illustrated through the growing popularity of Model Cards and two case studies of algorithmic impact assessment in China and Canada. Finally, we evaluate more recent proposals, including Reward Reports, as potential components of fully dynamic AI documentation protocols.

AI ethics is an emerging field with multiple, competing narratives about how to best solve the problem of building human values into machines. Two major approaches are focused on bias and compliance, respectively. But neither of these ideas fully encompasses ethics: using moral principles to decide how to act in a particular situation. Our method posits that the way data is labeled plays an essential role in the way AI behaves, and therefore in the ethics of machines themselves. The argument combines a fundamental insight from ethics (i.e. that ethics is about values) with our practical experience building and scaling machine learning systems. We want to build AI that is actually ethical by first addressing foundational concerns: how to build good systems, how to define what is good in relation to system architecture, and who should provide that definition. Building ethical AI creates a foundation of trust between a company and the users of that platform. But this trust is unjustified unless users experience the direct value of ethical AI. Until users have real control over how algorithms behave, something is missing in current AI solutions. This causes massive distrust in AI, and apathy towards AI ethics solutions. The scope of this paper is to propose an alternative path that allows for the plurality of values and the freedom of individual expression. Both are essential for realizing true moral character., Comment: 29 pages total, 1 table, 9 figures

This report is a methodological reflection on Z-Inspection$^{\small{\circledR}}$. Z-Inspection$^{\small{\circledR}}$ is a holistic process used to evaluate the trustworthiness of AI-based technologies at different stages of the AI lifecycle. It focuses, in particular, on the identification and discussion of ethical issues and tensions through the elaboration of socio-technical scenarios. It uses the general European Union's High-Level Expert Group's (EU HLEG) guidelines for trustworthy AI. This report illustrates for both AI researchers and AI practitioners how the EU HLEG guidelines for trustworthy AI can be applied in practice. We share the lessons learned from conducting a series of independent assessments to evaluate the trustworthiness of AI systems in healthcare. We also share key recommendations and practical suggestions on how to ensure a rigorous trustworthy AI assessment throughout the life-cycle of an AI system., Comment: On behalf of the Z-Inspection$^{\small{\circledR}}$ initiative (2022)

Autonomous Vehicles (AVs) will have a transformative impact on society. Beyond the local safety and efficiency of individual vehicles, these effects will also change how people interact with the entire transportation system. This will generate a diverse range of large and foreseeable effects on social outcomes, as well as how those outcomes are distributed. However, the ability to control both the individual behavior of AVs and the overall flow of traffic also provides new affordances that permit AVs to control these effects. This comprises a problem of sociotechnical specification: the need to distinguish which essential features of the transportation system are in or out of scope for AV development. We present this problem space in terms of technical, sociotechnical, and social problems, and illustrate examples of each for the transport system components of social mobility, public infrastructure, and environmental impacts. The resulting research methodology sketches a path for developers to incorporate and evaluate more transportation system features within AV system components over time., Comment: Paper accepted for presentation at ICRA 2022 workshop "Fresh Perspectives on the Future of Autonomous Driving"

Building systems that are good for society in the face of complex societal effects requires a dynamic approach. Recent approaches to machine learning (ML) documentation have demonstrated the promise of discursive frameworks for deliberation about these complexities. However, these developments have been grounded in a static ML paradigm, leaving the role of feedback and post-deployment performance unexamined. Meanwhile, recent work in reinforcement learning has shown that the effects of feedback and optimization objectives on system behavior can be wide-ranging and unpredictable. In this paper we sketch a framework for documenting deployed and iteratively updated learning systems, which we call Reward Reports. Taking inspiration from various contributions to the technical literature on reinforcement learning, we outline Reward Reports as living documents that track updates to design choices and assumptions behind what a particular automated system is optimizing for. They are intended to track dynamic phenomena arising from system deployment, rather than merely static properties of models or data. After presenting the elements of a Reward Report, we discuss a concrete example: Meta's BlenderBot 3 chatbot. Several others for game-playing (DeepMind's MuZero), content recommendation (MovieLens), and traffic control (Project Flow) are included in the appendix.

In the long term, reinforcement learning (RL) is considered by many AI theorists to be the most promising path to artificial general intelligence. This places RL practitioners in a position to design systems that have never existed before and lack prior documentation in law and policy. Public agencies could intervene on complex dynamics that were previously too opaque to deliberate about, and long-held policy ambitions would finally be made tractable. In this whitepaper we illustrate this potential and how it might be technically enacted in the domains of energy infrastructure, social media recommender systems, and transportation. Alongside these unprecedented interventions come new forms of risk that exacerbate the harms already generated by standard machine learning tools. We correspondingly present a new typology of risks arising from RL design choices, falling under four categories: scoping the horizon, defining rewards, pruning information, and training multiple agents. Rather than allowing RL systems to unilaterally reshape human domains, policymakers need new mechanisms for the rule of reason, foreseeability, and interoperability that match the risks these systems pose. We argue that criteria for these choices may be drawn from emerging subfields within antitrust, tort, and administrative law. It will then be possible for courts, federal and state agencies, and non-governmental organizations to play more active roles in RL specification and evaluation. Building on the "model cards" and "datasheets" frameworks proposed by Mitchell et al. and Gebru et al., we argue the need for Reward Reports for AI systems. Reward Reports are living documents for proposed RL deployments that demarcate design choices., Comment: 60 pages

As AI systems are integrated into high stakes social domains, researchers now examine how to design and operate them in a safe and ethical manner. However, the criteria for identifying and diagnosing safety risks in complex social contexts remain unclear and contested. In this paper, we examine the vagueness in debates about the safety and ethical behavior of AI systems. We show how this vagueness cannot be resolved through mathematical formalism alone, instead requiring deliberation about the politics of development as well as the context of deployment. Drawing from a new sociotechnical lexicon, we redefine vagueness in terms of distinct design challenges at key stages in AI system development. The resulting framework of Hard Choices in Artificial Intelligence (HCAI) empowers developers by 1) identifying points of overlap between design decisions and major sociotechnical challenges; 2) motivating the creation of stakeholder feedback channels so that safety issues can be exhaustively addressed. As such, HCAI contributes to a timely debate about the status of AI development in democratic societies, arguing that deliberation should be the goal of AI Safety, not just the procedure by which it is ensured., Comment: Pre-print. Shorter versions published at Neurips 2019 Workshop on AI for Social Good and Conference on AI, Ethics and Society 2020

The development of artificial intelligence (AI) technologies has far exceeded the investigation of their relationship with society. Sociotechnical inquiry is needed to mitigate the harms of new technologies whose potential impacts remain poorly understood. To date, subfields of AI research develop primarily individual views on their relationship with sociotechnics, while tools for external investigation, comparison, and cross-pollination are lacking. In this paper, we propose four directions for inquiry into new and evolving areas of technological development: value--what progress and direction does a field promote, optimization--how the defined system within a problem formulation relates to broader dynamics, consensus--how agreement is achieved and who is included in building it, and failure--what methods are pursued when the problem specification is found wanting. The paper provides a lexicon for sociotechnical inquiry and illustrates it through the example of consumer drone technology., Comment: 9 pages, 1 figure

Despite interest in communicating ethical problems and social contexts within the undergraduate curriculum to advance Public Interest Technology (PIT) goals, interventions at the graduate level remain largely unexplored. This may be due to the conflicting ways through which distinct Artificial Intelligence (AI) research tracks conceive of their interface with social contexts. In this paper we track the historical emergence of sociotechnical inquiry in three distinct subfields of AI research: AI Safety, Fair Machine Learning (Fair ML) and Human-in-the-Loop (HIL) Autonomy. We show that for each subfield, perceptions of PIT stem from the particular dangers faced by past integration of technical systems within a normative social order. We further interrogate how these histories dictate the response of each subfield to conceptual traps, as defined in the Science and Technology Studies literature. Finally, through a comparative analysis of these currently siloed fields, we present a roadmap for a unified approach to sociotechnical graduate pedagogy in AI., Comment: 8 Pages

We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billiards to some fundamental problems of statistical physics and their mathematically rigorous derivations in the framework of classical Hamiltonian systems., Comment: 50 pages, 3 figures, to appear in Pure and Applied Functional Analysis

Research in Theoretical Quantum Gravity has continued expansively even as it has become detached from classic arbiters of research such as direct empirical falsification. This makes it an interesting test case for social-scientific theories of what motivates and mediates contemporary scientific research and the nature of scientific objectivity. For our empirical investigation, we conducted 50 semi-structured interviews with researchers in the rival camps of String Theory and Loop Quantum Gravity, coded a subset for reoccurring themes, and subjected the resulting data to statistical analysis. Theoretically, we mobilize aspects of Daston and Galison's depiction of the scientific self and its relation to epistemic virtues, Pierre Bourdieu's field-centered account of social space, and Kantian notions of aesthetics in order to delineate the subjective tastes and the related process of collective consensus-making in contemporary quantum gravity research. We make two key contributions. First, our analysis sheds light on the inner workings of the field by connecting its internal epistemic struggles with relevant social-scientific theories. For example, we are able to suggest an explanation for how one approach, String Theory, has become so dominant. Second, our application of theories of social reproduction to the substance of scientific inquiry merits some substantive generalizations to Daston and Galison's framework. Most significantly, we propose as an addendum to their progression the notion of objectivity through intersubjectivity: objectivity obtained not through the suppression of the self but by its (regulated) pluralistic expression and performance., Comment: 15 pages, 10 figures

With the recent wave of progress in artificial intelligence (AI) has come a growing awareness of the large-scale impacts of AI systems, and recognition that existing regulations and norms in industry and academia are insufficient to ensure responsible AI development. In order for AI developers to earn trust from system users, customers, civil society, governments, and other stakeholders that they are building AI responsibly, they will need to make verifiable claims to which they can be held accountable. Those outside of a given organization also need effective means of scrutinizing such claims. This report suggests various steps that different stakeholders can take to improve the verifiability of claims made about AI systems and their associated development processes, with a focus on providing evidence about the safety, security, fairness, and privacy protection of AI systems. We analyze ten mechanisms for this purpose--spanning institutions, software, and hardware--and make recommendations aimed at implementing, exploring, or improving those mechanisms.

Smart cities solutions are often monolithically implemented, from sensors data handling through to the provided services. The same challenges are regularly faced by different developers, for every new solution in a new city. Expertise and know-how can be re-used and the effort shared. In this article we present the methodologies to minimize the efforts of implementing new smart city solutions and maximizing the sharing of components. The final target is to have a live technical community of smart city application developers. The results of this activity comes from the implementation of 35 city services in 27 cities between Europe and South Korea. To share efforts, we encourage developers to devise applications using a modular approach. Single-function components that are re-usable by other city services are packaged and published as standalone components, named Atomic Services. We identify 15 atomic services addressing smart city challenges in data analytics, data evaluation, data integration, data validation, and visualization. 38 instances of the atomic services are already operational in several smart city services. We detail in this article, as atomic service examples, some data predictor components. Furthermore, we describe real-world atomic services usage in the scenarios of Santander and three Danish cities. The resulting atomic services also generate a side market for smart city solutions, allowing expertise and know-how to be re-used by different stakeholders., Comment: 8 pages, 9 figures, 4 Tables, to be published in IEEE IoT Journal

As AI systems become prevalent in high stakes domains such as surveillance and healthcare, researchers now examine how to design and implement them in a safe manner. However, the potential harms caused by systems to stakeholders in complex social contexts and how to address these remains unclear. In this paper, we explain the inherent normative uncertainty in debates about the safety of AI systems. We then address this as a problem of vagueness by examining its place in the design, training, and deployment stages of AI system development. We adopt Ruth Chang's theory of intuitive comparability to illustrate the dilemmas that manifest at each stage. We then discuss how stakeholders can navigate these dilemmas by incorporating distinct forms of dissent into the development pipeline, drawing on Elizabeth Anderson's work on the epistemic powers of democratic institutions. We outline a framework of sociotechnical commitments to formal, substantive and discursive challenges that address normative uncertainty across stakeholders, and propose the cultivation of related virtues by those responsible for development., Comment: To be presented at the AI for Social Good workshop at NeurIPS 2019

Machine learning (ML) is increasingly deployed in real world contexts, supplying actionable insights and forming the basis of automated decision-making systems. While issues resulting from biases pre-existing in training data have been at the center of the fairness debate, these systems are also affected by technical and emergent biases, which often arise as context-specific artifacts of implementation. This position paper interprets technical bias as an epistemological problem and emergent bias as a dynamical feedback phenomenon. In order to stimulate debate on how to change machine learning practice to effectively address these issues, we explore this broader view on bias, stress the need to reflect on epistemology, and point to value-sensitive design methodologies to revisit the design and implementation process of automated decision-making systems., Comment: Presented at the 2018 Workshop on Fairness, Accountability and Transparency in Machine Learning during ICML 2018, Stockholm, Sweden

A process based on the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice cells share their energies among many identical degrees of freedom while, in each cell, only two of them are associated with energy exchanges connecting neighbouring cells. It is shown that, up to dimensional constants, the heat conductivity is half the interaction rate, regardless of the degrees of freedom. Moreover, as this number becomes large, correlations between the energy variables involved in the exchanges vanish. In this regime, the process thus boils down to the time-evolution of the local temperatures which is prescribed by the discrete heat equation., Comment: 7 pages, 3 figures

I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different temperatures, a systematic characterization of their non-equilibrium stationary states. These arguments avoid resorting to the analysis of a dual process and yield a straightforward derivation of Fourier's law, as well as higher-order static correlations, such as the covariant matrix. The transposition of these results to families of gradient models generalizing the KMP model is established and specific cases are examined., Comment: 26 pages

We present a systematic computation of the heat conductivity of the Markov jump process modeling the energy exchanges in an array of locally confined hard spheres at the conduction threshold. Based on a variational formula [Sasada M. 2016, {\it Thermal conductivity for stochastic energy exchange models}, arXiv:1611.08866], explicit upper bounds on the conductivity are derived, which exhibit a rapid power-law convergence towards an asymptotic value. We thereby conclude that the ratio of the heat conductivity to the energy exchange frequency deviates from its static contribution by a small negative correction, its dynamic contribution, evaluated to be $-0.000\,373$ in dimensionless units. This prediction is corroborated by kinetic Monte Carlo simulations which were substantially improved compared to earlier results., Comment: 33 pages, minor revisions

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator., Comment: 23 pages, 6 figures

Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times leads to a description of the process in terms of multiple states, whose distributions evolve according to a set of delay differential equations, amenable to analytic treatment. We obtain an exact expression of the mean squared displacement associated with such processes and discuss the emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive (subballistic) transport, emphasizing, in the latter case, the effect of initial conditions on the transport coefficients. Of particular interest is the case of rare ballistic propagation, in which case a regime of superdiffusion may lurk underneath one of normal diffusion., Comment: 27 pages, 4 figures

We study diffusion on a periodic billiard table with infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a L\'evy walk combining exponentially-distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [Phys. Rev. Lett. 50, 1959 (1983)]., Comment: 5 pages, 3 figures

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker, we are led to a description of such L\'evy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models., Comment: 5 pages, 2 figures. New references added

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions., Comment: 10 pages, 4 figures

This is a comment on [G. Knight and R. Klages, Phys. Rev. E 84, 041135 (2011); also available at arXiv:1107.5293v2 [math-ph]].

We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized., Comment: Submitted to Chaos, special issue "Statistical Mechanics and Billiard-Type Dynamical Systems"

Results concerning the statists of $r$-adic processes and their fractal properties are reviewed. The connection between singular eigenstates of the statistical evolution of such processes and popular fractal curves is emphasized., Comment: Submitted as part of a volume honoring the memory of Shuichi Tasaki

We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study a billiard model, namely a three-dimensional periodic Lorentz gas. The geometry of the model is studied in order to find the regimes in which it exhibits normal diffusion. In this regime, we calculate numerically the transition probabilities between cells to compare the persistent random-walk approximation with simulation results for the diffusion coefficient., Comment: 17 pages, 10 figures

We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by models of particles interacting via a string-type mechanism, and confined by hard walls. The combination of these elements may give rise to a defocusing mechanism, similar to that in two dimensions, which allows large chaotic regions in phase space. The remaining part of phase space is associated with marginally stable behaviour. In fact periodic orbits in these systems generically come in continuous parametric families, sociated with a pair of parabolic eigen-directions: the periodic orbits are unstable in the presence of a defocusing mechanism, but marginally stable otherwise. By performing the stability analysis of families of periodic orbits at a nonlinear level, we establish the conditions under which families are nonlinearly stable or unstable. As a result, we identify regions in the parameter space of the models which admit non-linearly stable oscillations in the form of whispering gallery modes. Where no families of periodic orbits are stable, the billiards are completely chaotic, i.e.\ the Lyapunov exponents of the billiard map are non-zero., Comment: 51 pages, 31 figures

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder and several planes; the combination of these elements may give rise to defocusing, allowing large chaotic regions in phase space. By studying families of marginally-stable periodic orbits that populate the residual part of phase space, we identify conditions under which a nonlinear instability mechanism arises in their vicinity. For particular geometries, this mechanism rather induces stable nonlinear oscillations, including in the form of whispering-gallery modes., Comment: 4 pages, 4 figures

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with two-step memory on different classes of one-, two- and higher-dimensional lattices., Comment: 27 pages, 2 figures

In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of ``persistence'' on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects, using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from., Comment: 7 pages, 7 figures

We study heat transport in a class of stochastic energy exchange systems that characterize the interactions of networks of locally trapped hard spheres under the assumption that neighbouring particles undergo rare binary collisions. Our results provide an extension to three-dimensional dynamics of previous ones applying to the dynamics of confined two-dimensional hard disks [Gaspard P & Gilbert T On the derivation of Fourier's law in stochastic energy exchange systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity is here again given by the frequency of energy exchanges. Moreover the expression of the stochastic kernel which specifies the energy exchange dynamics is simpler in this case and therefore allows for faster and more extensive numerical computations., Comment: 21 pages, 5 figures

Galton boards are models of deterministic diffusion in a uniform external field, akin to driven periodic Lorentz gases, here considered in the absence of dissipation mechanism. Assuming a cylindrical geometry with axis along the direction of the external field, the two-dimensional board becomes a model for one-dimensional mass transport along the direction of the external field. This is a purely diffusive process which admits fractal non-equilibrium stationary states under flux boundary conditions. Analytical results are obtained for the statistics of multi-baker maps modeling such a non-uniform diffusion process. A correspondence is established between the local phase-space statistics and their macroscopic counter-parts. The fractality of the invariant state is shown to be responsible for the positiveness of the entropy production rate., Comment: Second of two papers, 17 double column pages, 10 figures

Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with particle reservoirs at their boundaries. We study the macroscopic limits of these systems and establish a correspondence between the thermodynamics of the macroscopic diffusion process and the fractality of the stationary states that characterize the phase-space statistics. In particular the entropy production rate is recovered from first principles using a formalism due to Gaspard [J. Stat. Phys. 88, 1215 (1997)]. This article is the first of two; the second article considers the influence of a uniform external field on such systems., Comment: First of two papers. 14 double column pages, 7 figures

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical properties and establish the conditions under which their equilibrium measures have a product structure, i.e. factorises in a symmetric form. When these conditions are not verified, the equilibrium measure does not have a product form and therefore provides additional information on the statistical properties of theses maps. This is the case of anti-symmetric cusp maps, which have an intermittent fixed point and yet have uniform invariant measures on the unit interval. We construct the invariant density of the corresponding two-dimensional triangular map and prove that it exhibits a singularity at the intermittent fixed point., Comment: 15 pages, 3 figures

We present a detailed derivation of Fourier's law in a class of stochastic energy exchange systems that naturally characterize two-dimensional mechanical systems of locally confined particles in interaction. The stochastic systems consist of an array of energy variables which can be partially exchanged among nearest neighbours at variable rates. We provide two independent derivations of the thermal conductivity and prove this quantity is identical to the frequency of energy exchanges. The first derivation relies on the diffusion of the Helfand moment, which is determined solely by static averages. The second approach relies on a gradient expansion of the probability measure around a non-equilibrium stationary state. The linear part of the heat current is determined by local thermal equilibrium distributions which solve a Boltzmann-like equation. A numerical scheme is presented with computations of the conductivity along our two methods. The results are in excellent agreement with our theory., Comment: 19 pages, 5 figures, to appear in Journal of Statistical Mechanics (JSTAT)

We study the transport properties of a large class of locally confined Hamiltonian systems, in which neighboring particles interact through hard core elastic collisions. When these collisions become rare and the systems large, we derive a Boltzmann-like equation for the evolution of the probability densities. We solve this equation in the linear regime and compute the heat conductivity from a Green-Kubo formula. The validity of our approach is demonstated by comparing our predictions to the results of numerical simulations performed on a new class of high-dimensional defocusing chaotic billiards., Comment: 4 pages, 2 color figures

We present a first-principles study of heat conduction in a class of models which exhibit a new multi-step local thermalization mechanism which gives rise to Fourier's law. Local thermalization in our models occurs as the result of binary collisions among locally confined gas particles. We explore the conditions under which relaxation to local equilibrium, which involves no energy exchange, takes place on time scales shorter than that of the binary collisions which induce local thermalization. The role of this mechanism in multi-phase material systems such as aerogels is discussed., Comment: 4 pages, 3 color figures, to appear in Physical Review Letters

We consider the motion of many confined billiard balls in interaction and discuss their transport and chaotic properties. In spite of the absence of mass transport, due to confinement, energy transport can take place through binary collisions between neighbouring particles. We explore the conditions under which relaxation to local equilibrium occurs on time scales much shorter than that of binary collisions, which characterize the transport of energy, and subsequent relaxation to local thermal equilibrium. Starting from the pseudo-Liouville equation for the time evolution of phase-space distributions, we derive a master equation which governs the energy exchange between the system constituents. We thus obtain analytical results relating the transport coefficient of thermal conductivity to the frequency of collision events and compute these quantities. We also provide estimates of the Lyapunov exponents and Kolmogorov-Sinai entropy under the assumption of scale separation. The validity of our results is confirmed by extensive numerical studies., Comment: fixed figs. 12 & 13. Version to appear in New J. Phys

We study a particle moving at unit speed in a self-similar Lorentz billiard channel; the latter consists of an infinite sequence of cells which are identical in shape but growing exponentially in size, from left to right. We present numerical computation of the drift term in this system and establish the logarithmic periodicity of the corrections to the average drift.

The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonically according to their indices. This special geometry induces a nonequilibrium stationary state with particles flowing steadily from the small to the large scales. The corresponding invariant measure has fractal properties reflected by the phase-space contraction rate of the dynamics restricted to a single cell with appropriate boundary conditions. In the near-equilibrium limit, we find numerical agreement between this quantity and the entropy production rate as specified by thermodynamics.

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries.

We present numerical evidence supporting the validity of the Gallavotti-Cohen Fluctuation Theorem applied to the driven Lorentz gas with Nos\'e-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force, in the limit where it is small., Comment: 4 pages, 3 figures