IA Scholar Query: Monotonic evolution: an alternative to induction variable substitution for dependence analysis.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgFri, 30 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Runtime Complexity Bounds Using Squeezers
https://scholar.archive.org/work/rl374t3unrghnc7chpb4a65oie
Determining upper bounds on the time complexity of a program is a fundamental problem with a variety of applications, such as performance debugging, resource certification, and compile-time optimizations. Automated techniques for cost analysis excel at bounding the resource complexity of programs that use integer values and linear arithmetic. Unfortunately, they fall short when the complexity depends more intricately on the evolution of data during execution. In such cases, state-of-the-art analyzers have shown to produce loose bounds, or even no bound at all. We propose a novel technique that generalizes the common notion of recurrence relations based on ranking functions. Existing methods usually unfold one loop iteration and examine the resulting arithmetic relations between variables. These relations assist in establishing a recurrence that bounds the number of loop iterations. We propose a different approach, where we derive recurrences by comparing whole traces with whole traces of a lower rank, avoiding the need to analyze the complexity of intermediate states. We offer a set of global properties, defined with respect to whole traces, that facilitate such a comparison and show that these properties can be checked efficiently using a handful of local conditions. To this end, we adapt state squeezers , an induction mechanism previously used for verifying safety properties. We demonstrate that this technique encompasses the reasoning power of bounded unfolding, and more. We present some seemingly innocuous, yet intricate, examples that previous tools based on cost relations and control flow analysis fail to solve, and that our squeezer-powered approach succeeds.Oren Ish-Shalom, Shachar Itzhaky, Noam Rinetzky, Sharon Shohamwork_rl374t3unrghnc7chpb4a65oieFri, 30 Sep 2022 00:00:00 GMTSession Coalgebras: A Coalgebraic View on Regular and Context-free Session Types
https://scholar.archive.org/work/7gwjvkyxsrbc5ldzvszual56sa
Compositional methods are central to the verification of software systems. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types, these type systems can statically check that channels in a program interact following a certain protocol—whether messages are exchanged in the intended order. In this article, we put on our coalgebraic spectacles to investigate session types , a widely studied class of behavioural type systems. We provide a syntax-free description of session-based concurrency as states of coalgebras. As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation enables us to derive a decidable type system with subtyping for the π-calculus, in which the states of a coalgebra will serve as channel protocols. Going full circle, we exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective coincide with existing ones. We further apply to session coalgebras the coalgebraic approach to regular languages via the so-called rational fixed point, inspired by the trinity of automata, regular languages, and regular expressions with session coalgebras, rational fixed point, and session types, respectively. We establish a suitable restriction on session coalgebras that determines a similar trinity, and reveals the mismatch between usual session types and our syntax-free coalgebraic approach. Furthermore, we extend our coalgebraic approach to account for context-free session types, by equipping session coalgebras with a stack.Alex C. Keizer, Henning Basold, Jorge A. Pérezwork_7gwjvkyxsrbc5ldzvszual56saFri, 30 Sep 2022 00:00:00 GMTExploring the parameter space of MagLIF implosions using similarity scaling. III. Rise-time scaling
https://scholar.archive.org/work/gcqf7f2c4bggpn5n6nxasaqkdi
Magnetized Liner Inertial Fusion (MagLIF) is a z-pinch magneto-inertial-fusion (MIF) concept studied on the Z Machine at Sandia National Laboratories. Two important metrics characterizing current delivery to a z-pinch load are the peak current and the current-rise time, which is roughly the time interval to reach peak current. It is known that, when driving a z-pinch load with a longer current-rise time, the performance of the z-pinch decreases. However, a theory to understand and quantify this effect is still lacking. In this paper, we utilize a framework based on similarity scaling to analytically investigate the variations in performance of MagLIF loads when varying the current-rise time, or equivalently, the implosion timescale. To maintain similarity between the implosions, we provide the scaling prescriptions of the experimental input parameters defining a MagLIF load and derive the scaling laws for the stagnation conditions and for various performance metrics. We compare predictions of the theory to 2D numerical simulations using the radiation, magneto-hydrodynamic code HYDRA. For several metrics, we find acceptable agreement between the theory and simulations. Our results show that the voltage near the MagLIF load follows a weak scaling law φ_ load∝ t_φ^-0.12 with respect to the characteristic timescale t_φ of the voltage source, instead of the ideal φ_ load∝ t_φ^-1 scaling. This occurs because the imploding height of the MagLIF load must increase to preserve end losses. As a consequence of the longer imploding liners, the required total laser preheat energy and delivered electric energy increase. Overall, this study may help understand the trade-offs of the MagLIF design space when considering future pulsed-power generators with shorter and longer current-rise times.D. E. Ruiz, P. F. Schmit, M. R. Weis, K. J. Peterson, M. K. Matzenwork_gcqf7f2c4bggpn5n6nxasaqkdiThu, 29 Sep 2022 00:00:00 GMTNoise in Biomolecular Systems: Modeling, Analysis, and Control Implications
https://scholar.archive.org/work/d2oa2hquunbwjcahn3bsbabvpy
While noise is generally associated with uncertainties and often has a negative connotation in engineering, living organisms have evolved to adapt to (and even exploit) such uncertainty to ensure the survival of a species or implement certain functions that would have been difficult or even impossible otherwise. In this article, we review the role and impact of noise in systems and synthetic biology, with a particular emphasis on its role in the genetic control of biological systems, an area we refer to as Cybergenetics. The main modeling paradigm is that of stochastic reaction networks, whose applicability goes beyond biology, as these networks can represent any population dynamics system, including ecological, epidemiological, and opinion dynamics networks. We review different ways to mathematically represent these systems, and we notably argue that the concept of ergodicity presents a particularly suitable way to characterize their stability. We then discuss noise-induced properties and show that noise can be both an asset and a nuisance in this setting. Finally, we discuss recent results on (stochastic) Cybergenetics and explore their relationships to noise. Along the way, we detail the different technical and biological constraints that need to be respected when designing synthetic biological circuits. Finally, we discuss the concepts, problems, and solutions exposed in the article; raise criticisms and concerns about current ideas and approaches; suggest current (open) problems with potential solutions; and provide some ideas for future research directions.Corentin Briat, Mustafa Khammashwork_d2oa2hquunbwjcahn3bsbabvpyWed, 28 Sep 2022 00:00:00 GMTEssays in climate finance
https://scholar.archive.org/work/b5xhu7y7kbfz5oxznbj4nzq26e
This thesis investigates the behaviour of firms in relation to \emph{climate-transition} events, so-called events that occur as part of the transition to a green economy to prevent climate change. The first chapter looks at the current development of the sustainable finance market to study how green securities should be optimally designed and whether measurement and information frictions can explain observed cross-sectional issuance patterns. The second chapter exploits a climate regulatory announcement to study how firms' beliefs about climate regulation affect their emissions abatement plans and how they interact with cross-firm reputation externalities. The third chapter makes use of an environmental policy implemented in the United Kingdom to study the cost-effectiveness of carbon pricing policies subject to carbon leakage risk and asymmetric information.Federica Zeni, Tarun Ramadorai, Ansgar Waltherwork_b5xhu7y7kbfz5oxznbj4nzq26eWed, 28 Sep 2022 00:00:00 GMTArtificial Intelligence and Advanced Materials
https://scholar.archive.org/work/tkf566mg6zf77a7xan6anloxvu
Artificial intelligence is gaining strength and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems and processes can be devised and optimized thanks to machine learning techniques and such progress can be turned into in-novative computing platforms. Future materials scientists will profit from understanding how machine learning can boost the conception of advanced materials. This review covers aspects of computation from the fundamentals to directions taken and repercussions produced by compu-tation to account for the origins, procedures and applications of artificial intelligence. Machine learning and its methods are reviewed to provide basic knowledge on its implementation and its potential. The materials and systems used to implement artificial intelligence with electric charges are finding serious competition from other information carrying and processing agents. The impact these techniques are having on the inception of new advanced materials is so deep that a new paradigm is developing where implicit knowledge is being mined to conceive materi-als and systems for functions instead of finding applications to found materials. How far this trend can be carried is hard to fathom as exemplified by the power to discover unheard of mate-rials or physical laws buried in data.Cefe Lópezwork_tkf566mg6zf77a7xan6anloxvuWed, 28 Sep 2022 00:00:00 GMTUniformly Expanding Coupled Maps: Self-Consistent Transfer Operators and Propagation of Chaos
https://scholar.archive.org/work/ahazqyj6nrc7vnyhyjjqcisvae
In this paper we study systems of N uniformly expanding coupled maps when N is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this approximation explicitly with respect to N. Using this result, we prove that uniformly expanding coupled maps satisfy propagation of chaos when N→∞, and characterize the absolutely continuous invariant measures for the finite dimensional system. The main working assumption is that the expansion is not too small and the strength of the interactions is not too large, although both can be of order one. In contrast with previous approaches, we do not require the coupled maps and the interactions to be identical. The technical advances that allow us to describe the system are: the introduction of a framework to study the evolution of conditional measures along some non-invariant foliations where the dependence of all estimates on the dimension is explicit; and the characterization of an invariant class of measures close to products that satisfy exponential concentration inequalities.Matteo Tanziwork_ahazqyj6nrc7vnyhyjjqcisvaeTue, 27 Sep 2022 00:00:00 GMTHigh-Dimensional Geometric Streaming in Polynomial Space
https://scholar.archive.org/work/btmazlynqvc77kwthohpbovcia
Many existing algorithms for streaming geometric data analysis have been plagued by exponential dependencies in the space complexity, which are undesirable for processing high-dimensional data sets. In particular, once d≥log n, there are no known non-trivial streaming algorithms for problems such as maintaining convex hulls and Löwner-John ellipsoids of n points, despite a long line of work in streaming computational geometry since [AHV04]. We simultaneously improve these results to poly(d,log n) bits of space by trading off with a poly(d,log n) factor distortion. We achieve these results in a unified manner, by designing the first streaming algorithm for maintaining a coreset for ℓ_∞ subspace embeddings with poly(d,log n) space and poly(d,log n) distortion. Our algorithm also gives similar guarantees in the online coreset model. Along the way, we sharpen results for online numerical linear algebra by replacing a log condition number dependence with a log n dependence, answering a question of [BDM+20]. Our techniques provide a novel connection between leverage scores, a fundamental object in numerical linear algebra, and computational geometry. For ℓ_p subspace embeddings, we give nearly optimal trade-offs between space and distortion for one-pass streaming algorithms. For instance, we give a deterministic coreset using O(d^2log n) space and O((dlog n)^1/2-1/p) distortion for p>2, whereas previous deterministic algorithms incurred a poly(n) factor in the space or the distortion [CDW18]. Our techniques have implications in the offline setting, where we give optimal trade-offs between the space complexity and distortion of subspace sketch data structures. To do this, we give an elementary proof of a "change of density" theorem of [LT80] and make it algorithmic.David P. Woodruff, Taisuke Yasudawork_btmazlynqvc77kwthohpbovciaTue, 27 Sep 2022 00:00:00 GMTA posteriori estimates for the stochastic total variation flow
https://scholar.archive.org/work/4fsklfbdxvdurg54ycj5o6ptne
We derive a posteriori error estimates for a fully discrete time-implicit finite element approximation of the stochastic total variaton flow (STVF) with additive space time noise. The estimates are first derived for an implementable fully discrete approximation of a regularized stochastic total variation flow. We then show that the derived a posteriori estimates remain valid for the unregularized flow up to a perturbation term that can be controlled by the regularization parameter. Based on the derived a posteriori estimates we propose a pathwise algorithm for the adaptive space-time refinement and perform numerical simulation for the regularized STVF to demonstrate the behavior of the proposed algorithm.Ľubomír Baňas, André Wilkework_4fsklfbdxvdurg54ycj5o6ptneTue, 27 Sep 2022 00:00:00 GMTPrinciples Of Heliophysics: a textbook on the universal processes behind planetary habitability
https://scholar.archive.org/work/v2zqk34khrabtaqqb3zmwqkhpa
Heliophysics is the system science of the physical connections between the Sun and the solar system. As the physics of the local cosmos, it embraces space weather and planetary habitability. The wider view of comparative heliophysics forms a template for conditions in exoplanetary systems and provides a view over time of the aging Sun and its magnetic activity, of the heliosphere in different settings of the interstellar medium and subject to stellar impacts, of the space physics over evolving planetary dynamos, and of the long-term influence on planetary atmospheres by stellar radiation and wind. Based on a series of NASA-funded summer schools for early-career researchers, this textbook is intended for students in physical sciences in later years of their university training and for beginning graduate students in fields of solar, stellar, (exo-)planetary, and planetary-system sciences. The book emphasizes universal processes from a perspective that draws attention to what provides Earth (and similar (exo-)planets) with a relatively stable setting in which life as we know it could thrive. The text includes 200 "Activities" in the form of exercises, explorations, literature readings, "what if" challenges, and group discussion topics; many of the Activities provide additional information complementing the main text. Solutions and discussions are included in an Appendix for a selection of the exercises.Karel Schrijver, Fran Bagenal, Tim Bastian, Juerg Beer, Mario Bisi, Tom Bogdan, Steve Bougher, David Boteler, Dave Brain, Guy Brasseur, Don Brownlee, Paul Charbonneau, Ofer Cohen, Uli Christensen, Tom Crowley, Debrah Fischer, Terry Forbes, Tim Fuller-Rowell, Marina Galand, Joe Giacalone, George Gloeckler, Jack Gosling, Janet Green, Nick Gross, Steve Guetersloh, Viggo Hansteen, Lee Hartmann, Mihaly Horanyi, Hugh Hudson, Norbert Jakowski, Randy Jokipii, Margaret Kivelson, Dietmar Krauss-Varban, Norbert Krupp, Judith Lean, Jeff Linsky, Dana Longcope, Daniel Marsh, Mark Miesch, Mark Moldwin, Luke Moore, Sten Odenwald, Merav Opher, Rachel Osten, Matthias Rempel, Hauke Schmidt, George Siscoe, Dave Siskind, Chuck Smith, Stan Solomon, Tom Stallard, Sabine Stanley, Jan Sojka, Kent Tobiska, Frank Toffoletto, Alan Tribble, Vytenis Vasyliunas, Richard Walterscheid, Ji Wang, Brian Wood, Tom Woods, Neal Zappwork_v2zqk34khrabtaqqb3zmwqkhpaTue, 27 Sep 2022 00:00:00 GMTDynamics of COVID-19 Using SEIQR Epidemic Model
https://scholar.archive.org/work/zzl3w37zqfc7flvic3s4tzahfa
The major goal of this study is to create an optimal technique for managing COVID-19 spread by transforming the SEIQR model into a dynamic (multistage) programming problem with continuous and discrete time-varying transmission rates as optimizing variables. We have developed an optimal control problem for a discrete-time, deterministic susceptible class (S), exposed class (E), infected class (I), quarantined class (Q), and recovered class (R) epidemic with a finite time horizon. The problem involves finding the minimum objective function of a controlled process subject to the constraints of limited resources. For our model, we present a new technique based on dynamic programming problem solutions that can be used to minimize infection rate and maximize recovery rate. We developed suitable conditions for obtaining monotonic solutions and proposed a dynamic programming model to obtain optimal transmission rate sequences. We explored the positivity and unique solvability nature of these implicit and explicit time-discrete models. According to our findings, isolating the affected humans can limit the danger of COVID-19 spreading in the future.N. Avinash, G. Britto Antony Xavier, Ammar Alsinai, Hanan Ahmed, V. Rexma Sherine, P. Chellamani, Ali Sajidwork_zzl3w37zqfc7flvic3s4tzahfaMon, 26 Sep 2022 00:00:00 GMTDefects and Frustration in the Packing of Soft Balls
https://scholar.archive.org/work/67elapy57jfdtg63bzhtulxmla
This work introduces the Hookean-Voronoi energy, a minimal model for the packing of soft, deformable balls. This is motivated by recent studies of quasi-periodic equilibria arising from dense packings of diblock and star polymers. Restricting to the planar case, we investigate the equilibrium packings of identical, deformable objects whose shapes are determined by an N-site Voronoi tessellation of a periodic rectangle. We derive a reduced formulation of the system showing at equilibria each site must reside at the "max-center" of its associated Voronoi region and construct a family of ordered "single-string" minimizers whose cardinality is O(N^2). We identify sharp conditions under which the system admits a regular hexagonal tessellation and establish that in all cases the average energy per site is bounded below by that of a regular hexagon of unit size. However, numerical investigation of gradient flow of random initial data, reveals that for modest values of N the system preponderantly equilibrates to quasi-ordered states with low energy and large basins of attraction. For larger N the distribution of equilibria energies appears to approach a δ-function limit, whose energy is significantly higher than the ground state hexagon. This limit is possibly shaped by two mechanisms: a proliferation of moderate-energy disordered equilibria that block access of the gradient flow to lower energy quasi-ordered states and a rigid threshold on the maximum energy of stable states.Kenneth Jao, Keith Promislow, Samuel Sottilework_67elapy57jfdtg63bzhtulxmlaSun, 25 Sep 2022 00:00:00 GMTIn-context Learning and Induction Heads
https://scholar.archive.org/work/4omh6xao2zgo5lhlkaedddmgsa
"Induction heads" are attention heads that implement a simple algorithm to complete token sequences like [A][B] ... [A] -> [B]. In this work, we present preliminary and indirect evidence for a hypothesis that induction heads might constitute the mechanism for the majority of all "in-context learning" in large transformer models (i.e. decreasing loss at increasing token indices). We find that induction heads develop at precisely the same point as a sudden sharp increase in in-context learning ability, visible as a bump in the training loss. We present six complementary lines of evidence, arguing that induction heads may be the mechanistic source of general in-context learning in transformer models of any size. For small attention-only models, we present strong, causal evidence; for larger models with MLPs, we present correlational evidence.Catherine Olsson, Nelson Elhage, Neel Nanda, Nicholas Joseph, Nova DasSarma, Tom Henighan, Ben Mann, Amanda Askell, Yuntao Bai, Anna Chen, Tom Conerly, Dawn Drain, Deep Ganguli, Zac Hatfield-Dodds, Danny Hernandez, Scott Johnston, Andy Jones, Jackson Kernion, Liane Lovitt, Kamal Ndousse, Dario Amodei, Tom Brown, Jack Clark, Jared Kaplan, Sam McCandlish, Chris Olahwork_4omh6xao2zgo5lhlkaedddmgsaSat, 24 Sep 2022 00:00:00 GMTVortices in Bose-Einstein Condensates
https://scholar.archive.org/work/3xxk3e7e4zblflwlrzjjjrdw7m
This thesis surveys aspects of the very broad topic of vortex dynamics in Bose-Einstein condensates. The Gross-Pitaevskii equation (GPE) is an important and popular tool in this regard, and we discuss a number of its properties which are relevant to the study of vortex dynamics. Using the GPE, we explore the dynamics of point vortices in Bose-Einstein condensates, writing hydrodynamic relations we have not encountered elsewhere in the literature. For incompressible condensates, we pay particular attention to discussions of the structure of the Hamiltonian system, and we revisit the topic of linear stability analysis for a steadily rotating, regular polygon of vortices. Furthermore, geometric mechanics is a powerful tool in the study of fluid dynamics, and we make use of the language of geometric mechanics, in particular the Lie derivative, to gain insights into some of the consequences of describing superfluid dynamics using the GPE. We have not encountered the relations we have derived as a result of this effort elsewhere in the literature. The topics of vortex formation, general approaches to describing vortex dynamics and phonon emission are also discussed.Omofolarin Alex-Duduyemi, Henrik Jensenwork_3xxk3e7e4zblflwlrzjjjrdw7mThu, 22 Sep 2022 00:00:00 GMTThe Axiomatic Approach to Non-Classical Model Theory
https://scholar.archive.org/work/eis66kn4lvfj7ewxu3xnqlxzwy
Institution theory represents the fully axiomatic approach to model theory in which all components of logical systems are treated fully abstractly by reliance on category theory. Here, we survey some developments over the last decade or so concerning the institution theoretic approach to non-classical aspects of model theory. Our focus will be on many-valued truth and on models with states, which are addressed by the two extensions of ordinary institution theory known as L-institutions and stratified institutions, respectively. The discussion will include relevant concepts, techniques, and results from these two areas.Răzvan Diaconescuwork_eis66kn4lvfj7ewxu3xnqlxzwyWed, 21 Sep 2022 00:00:00 GMTComputation of Feedback Control Laws Based on Switched Tracking of Demonstrations
https://scholar.archive.org/work/zv5l24jvnvdg3edod76fvfoaui
A common approach in robotics is to learn tasks by generalizing from special cases given by a so-called demonstrator. In this paper, we apply this paradigm to a general control synthesis setting. We present an algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering ordinary differential equations into a goal set. The resulting feedback control law switches between the demonstrations that it uses as reference trajectories which results in a hybrid closed loop system. In comparison to the direct use of trajectory optimization as a control law, for example, in the form of model predictive control, this allows for a much simpler and more efficient implementation of the controller. The synthesis algorithm comes with rigorous convergence and optimality results, and computational experiments confirm its efficiency.Jiří Fejlek, Stefan Ratschanwork_zv5l24jvnvdg3edod76fvfoauiWed, 21 Sep 2022 00:00:00 GMTPrice Discrimination in International Airline Markets
https://scholar.archive.org/work/rj5ypwabd5c2bde5cwq2dxvls4
We develop a model of inter-temporal and intra-temporal price discrimination by monopoly airlines to study the ability of different discriminatory pricing mechanisms to increase efficiency and the associated distributional implications. To estimate the model, we use unique data from international airline markets with flight-level variation in prices across time, cabins, and markets and information on passengers' reasons for travel and time of purchase. The current pricing practice yields approximately 77% of the first-best welfare. The source of this inefficiency arises primarily from private information about passenger valuations, not dynamic uncertainty about demand. We also find that if airlines could discriminate between business and leisure passengers, total welfare would improve at the expense of business passenger surplus. Also, replacing the current pricing that involves screening passengers across cabin classes with offering a single cabin class has minimal effect on total welfare.Gaurab Aryal and Charles Murry and Jonathan W. Williamswork_rj5ypwabd5c2bde5cwq2dxvls4Mon, 19 Sep 2022 00:00:00 GMTLandscape evolution of the southeast Queensland dune fields
https://scholar.archive.org/work/mgmaa6jywfcothjga2pexr3d4e
The sub-tropical coastal dune fields of southeast Queensland, Australia are recognised for their outstanding beauty, cultural importance, and ecological diversity. Their soil and vegetation development have been intensively investigated and more recently, the geochronology of the dune fields has been expanded. However, there has been little focus on the evolution of the dune fields after the dunes stabilise. The aim of this thesis is to enhance our fundamental understanding of dune field evolution by evaluating the complete topographic development of the dunes from their emplacement (stabilisation) to maturity (denuded topography). Principals and concepts derived from hillslope geomorphology were used to determine styles and rates of landscape change. The Holocene section of the Cooloola Sand Mass (CSM) is the primary focus of this study, while Holocene dunes on K'gari (Fraser Island) were also investigated. The dune fields were selected because most of the major environmental factors contributing to landscape development in the Holocene can be constrained, and they contain one of the most complete coastal dunes sequences in the world. Quantitative topographic analyses from high-resolution digital elevation models with landscape evolution theories (linear and nonlinear sediment transport) were used to better describe and understand dune fields and dune landforms. Principally, the foundational idea that gravitationally driven transport processes smooth dune landforms to their base-levels thereby reducing mean local relief, was used. The concept that landscape smooths with time provides the framework to establish morphostratigraphical mapping, 2-D numerical modelling, and roughness-age modelling. From the geomorphological mapping it is observed that the SE Queensland dune fields are constructed of five Holocene (including active dunes) and four Pleistocene dune morphosequence units. Dunes and their units systematically smooth with time and this evolution is well explained using surface roughness (σC). It is demonst [...]Nicholas R. Patton, University Of Canterburywork_mgmaa6jywfcothjga2pexr3d4eFri, 16 Sep 2022 00:00:00 GMTLandauer vs. Nernst: What is the True Cost of Cooling a Quantum System?
https://scholar.archive.org/work/btr2l4kjjzctbiuetxzfoc26wi
Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, stating that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilised? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity. However, such optimal protocols require complex unitaries generated by an external work source. Restricting to unitaries that can be run solely via a heat engine, we derive a novel Carnot-Landauer limit, along with protocols for its saturation. This generalises Landauer's principle to a fully thermodynamic setting, leading to a unification with the third law and emphasising the importance of control in quantum thermodynamics.Philip Taranto, Faraj Bakhshinezhad, Andreas Bluhm, Ralph Silva, Nicolai Friis, Maximilian P. E. Lock, Giuseppe Vitagliano, Felix C. Binder, Tiago Debarba, Emanuel Schwarzhans, Fabien Clivaz, Marcus Huberwork_btr2l4kjjzctbiuetxzfoc26wiFri, 16 Sep 2022 00:00:00 GMTIsing model on random triangulations of the disk: phase transition
https://scholar.archive.org/work/pavuypmzzzfbznsk43tk4vcd3m
In [arXiv:1806.06668], we have studied the Boltzmann random triangulation of the disk coupled to an Ising model on its faces with Dobrushin boundary condition at its critical temperature. In this paper, we investigate the phase transition of this model by extending our previous results to arbitrary temperature: We compute the partition function of the model at all temperatures, and derive several critical exponents associated with the infinite perimeter limit. We show that the model has a local limit at any temperature, whose properties depend drastically on the temperature. At high temperatures, the local limit is reminiscent of the uniform infinite half-planar triangulation (UIHPT) decorated with a subcritical percolation. At low temperatures, the local limit develops a bottleneck of finite width due to the energy cost of the main Ising interface between the two spin clusters imposed by the Dobrushin boundary condition. This change can be summarized by a novel order parameter with a nice geometric meaning. In addition to the phase transition, we also generalize our construction of the local limit from the two-step asymptotic regime used in [arXiv:1806.06668] to a more natural diagonal asymptotic regime. We obtain in this regime a scaling limit related to the length of the main Ising interface, which coincides with predictions from the continuum theory of quantum surfaces (a.k.a.\ Liouville quantum gravity).Linxiao Chen, Joonas Turunenwork_pavuypmzzzfbznsk43tk4vcd3mThu, 15 Sep 2022 00:00:00 GMT