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  • 1.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Dynamic Distance Measure on Spaces of Isospectral Mixed Quantum States2013In: Entropy, E-ISSN 1099-4300, Vol. 15, no 9, p. 3688-3697Article in journal (Refereed)
    Abstract [en]

    Distance measures are used to quantify the extent to which information is preserved or altered by quantum processes, and thus are indispensable tools in quantum information and quantum computing. In this paper we propose a new distance measure for mixed quantum states, which we call the dynamic distance measure, and we show that it is a proper distance measure. The dynamic distance measure is defined in terms of a measurable quantity, which makes it suitable for applications. In a final section we compare the dynamic distance measure with the well-known Bures distance measure.

  • 2.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). School of Natural Sciences and Medicine, Ilia State University, Georgia; McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, USA.
    Protiti, Nousaba Nasrin
    Electromagnetic Conversion into Kinetic and Thermal Energies2023In: Entropy, E-ISSN 1099-4300, Vol. 25, no 9, article id 1270Article in journal (Refereed)
    Abstract [en]

    The conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating in the early universe at the end of inflation and before the emergence of the radiation-dominated era. We find that the conversion into kinetic and thermal energies is primarily the result of electric energy dissipation, while magnetic energy only plays a secondary role in this process. This means that since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges before the relevant length scales become stable.

  • 3. Diaz-Pachón, Daniel Andrés
    et al.
    Hössjer, Ola
    Stockholm University, Faculty of Science, Department of Mathematics.
    Assessing, Testing and Estimating the Amount of Fine-Tuning by Means of Active Information2022In: Entropy, E-ISSN 1099-4300, Vol. 24, no 10, article id 1323Article in journal (Refereed)
    Abstract [en]

    A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter θ that quantifies how much background information has been infused. A simple choice of this parameter is to use θf in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis–Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters θ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming.

  • 4.
    Hössjer, Ola
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Díaz-Pachón, Daniel Andrés
    Rao, J. Sunil
    A Formal Framework for Knowledge Acquisition: Going beyond Machine Learning2022In: Entropy, E-ISSN 1099-4300, Vol. 24, no 10, article id 1469Article in journal (Refereed)
    Abstract [en]

    Philosophers frequently define knowledge as justified, true belief. We built a mathematical framework that makes it possible to define learning (increasing number of true beliefs) and knowledge of an agent in precise ways, by phrasing belief in terms of epistemic probabilities, defined from Bayes’ rule. The degree of true belief is quantified by means of active information I+: a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent’s strength of belief in a true proposition has increased in comparison with the ignorant person (I+>0), or the strength of belief in a false proposition has decreased (I+<0). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds that correspond to parameters of a statistical model. This makes it possible to interpret learning as a hypothesis test for such a model, whereas knowledge acquisition additionally requires estimation of a true world parameter. Our framework of learning and knowledge acquisition is a hybrid between frequentism and Bayesianism. It can be generalized to a sequential setting, where information and data are updated over time. The theory is illustrated using examples of coin tossing, historical and future events, replication of studies, and causal inference. It can also be used to pinpoint shortcomings of machine learning, where typically learning rather than knowledge acquisition is in focus.

  • 5.
    Jafari-Mamaghani, Mehrdad
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Karolinska Institutet, Sweden.
    Tyrcha, Joanna
    Stockholm University, Faculty of Science, Department of Mathematics.
    Transfer Entropy Expressions for a Class of Non-Gaussian Distributions2014In: Entropy, E-ISSN 1099-4300, Vol. 16, no 3, p. 1743-1755Article in journal (Refereed)
    Abstract [en]

    Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I - IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

  • 6.
    Mathisen, Thomas
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Larson, Jonas
    Stockholm University, Faculty of Science, Department of Physics.
    Liouvillian of the Open STIRAP Problem2018In: Entropy, E-ISSN 1099-4300, Vol. 20, no 1, article id 20Article in journal (Refereed)
    Abstract [en]

    With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system's (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically.

  • 7. Meng, Xiangyi
    et al.
    Hu, Xinqi
    Tian, Yu
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). KTH, Sweden.
    Dong, Gaogao
    Lambiotte, Renaud
    Gao, Jianxi
    Havlin, Shlomo
    Percolation Theories for Quantum Networks2023In: Entropy, E-ISSN 1099-4300, Vol. 25, no 11, article id 1564Article, review/survey (Refereed)
    Abstract [en]

    Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called concurrence percolation, which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

  • 8. Padmanaban, Rajchandar
    et al.
    Bhowmik, Avit K.
    Stockholm University, Faculty of Science, Stockholm Resilience Centre.
    Cabral, Pedro
    Zamyatin, Alexander
    Almegdadi, Oraib
    Wang, Shuangao
    Modelling Urban Sprawl Using Remotely Sensed Data: A Case Study of Chennai City, Tamilnadu2017In: Entropy, E-ISSN 1099-4300, Vol. 19, no 4, article id 163Article in journal (Refereed)
    Abstract [en]

    Urban sprawl (US), propelled by rapid population growth leads to the shrinkage of productive agricultural lands and pristine forests in the suburban areas and, in turn, adversely affects the provision of ecosystem services. The quantification of US is thus crucial for effective urban planning and environmental management. Like many megacities in fast growing developing countries, Chennai, the capital of Tamilnadu and one of the business hubs in India, has experienced extensive US triggered by the doubling of total population over the past three decades. However, the extent and level of US has not yet been quantified and a prediction for future extent of US is lacking. We employed the Random Forest (RF) classification on Landsat imageries from 1991, 2003, and 2016, and computed six landscape metrics to delineate the extent of urban areas within a 10 km suburban buffer of Chennai. The level of US was then quantified using Renyi's entropy. A land change model was subsequently used to project land cover for 2027. A 70.35% expansion in urban areas was observed mainly towards the suburban periphery of Chennai between 1991 and 2016. The Renyi's entropy value for year 2016 was 0.9, exhibiting a two-fold level of US when compared to 1991. The spatial metrics values indicate that the existing urban areas became denser and the suburban agricultural, forests and particularly barren lands were transformed into fragmented urban settlements. The forecasted land cover for 2027 indicates a conversion of 13,670.33 ha (16.57% of the total landscape) of existing forests and agricultural lands into urban areas with an associated increase in the entropy value to 1.7, indicating a tremendous level of US. Our study provides useful metrics for urban planning authorities to address the social-ecological consequences of US and to protect ecosystem services.

  • 9. Schmitz, Georg J.
    et al.
    te Vrugt, Michael
    Haug-Warberg, Tore
    Ellingsen, Lodin
    Needham, Paul
    Stockholm University, Faculty of Humanities, Department of Philosophy.
    Wittkowski, Raphael
    Thermodynamics of an Empty Box2023In: Entropy, E-ISSN 1099-4300, Vol. 25, no 2, article id 315Article in journal (Refereed)
    Abstract [en]

    A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermody- namics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.

  • 10. Schunck, Florian
    et al.
    Wiedermann, Marc
    Heitzig, Jobst
    Donges, Jonathan
    Stockholm University, Faculty of Science, Stockholm Resilience Centre. Potsdam Institute for Climate Impact Research, Germany.
    A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse2024In: Entropy, E-ISSN 1099-4300, Vol. 26, no 2, article id 98Article in journal (Refereed)
    Abstract [en]

    In recent years, several global events have severely disrupted economies and social structures, undermining confidence in the resilience of modern societies. Examples include the COVID-19 pandemic, which brought unprecedented health challenges and economic disruptions, and the emergence of geopolitical tensions and conflicts that have further strained international relations and economic stability. While empirical evidence on the dynamics and drivers of past societal collapse is mounting, a process-based understanding of these dynamics is still in its infancy. Here, we aim to identify and illustrate the underlying drivers of such societal instability or even collapse. The inspiration for this work is Joseph Tainter’s theory of the “collapse of complex societies”, which postulates that the complexity of societies increases as they solve problems, leading to diminishing returns on complexity investments and ultimately to collapse. In this work, we abstract this theory into a low-dimensional and stylized model of two classes of networked agents, hereafter referred to as “laborers” and “administrators”. We numerically model the dynamics of societal complexity, measured as the fraction of “administrators”, which was assumed to affect the productivity of connected energy-producing “laborers”. We show that collapse becomes increasingly likely as the complexity of the model society continuously increases in response to external stresses that emulate Tainter’s abstract notion of problems that societies must solve. We also provide an analytical approximation of the system’s dominant dynamics, which matches well with the numerical experiments, and use it to study the influence on network link density, social mobility and productivity. Our work advances the understanding of social-ecological collapse and illustrates its potentially direct link to an ever-increasing societal complexity in response to external shocks or stresses via a self-reinforcing feedback.

  • 11.
    Stølevik Olsen, Kristian
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Heinrich-Heine-Universität, Germany.
    Hansen, Alex
    Grude Flekkøy, Eirik
    Hyper-Ballistic Superdiffusion of Competing Microswimmers2024In: Entropy, E-ISSN 1099-4300, Vol. 26, no 3, article id 274Article in journal (Refereed)
    Abstract [en]

    Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker-Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis.

  • 12.
    Tamm, Martin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Is Causality a Necessary Tool for Understanding Our Universe, or Is It a Part of the Problem?2021In: Entropy, E-ISSN 1099-4300, Vol. 23, no 7, article id 886Article in journal (Refereed)
    Abstract [en]

    In this paper, the concept of causality in physics is discussed. Causality is a necessary tool for the understanding of almost all physical phenomena. However, taking it as a fundamental principle may lead us to wrong conclusions, particularly in cosmology. Here, three very well-known problems-the Einstein-Podolsky-Rosen paradox, the accelerating expansion and the asymmetry of time-are discussed from this perspective. In particular, the implications of causality are compared to those of an alternative approach, where we instead take the probability space of all possible developments as the starting point.

  • 13.
    Tamm, Martin
    Stockholm University, Faculty of Science, Department of Mathematics.
    The Thermodynamical Arrow and the Historical Arrow; Are They Equivalent?2017In: Entropy, E-ISSN 1099-4300, Vol. 19, no 9, article id 455Article in journal (Refereed)
    Abstract [en]

    In this paper, the relationship between the thermodynamic and historical arrows of time is studied. In the context of a simple combinatorial model, their definitions are made more precise and in particular strong versions (which are not compatible with time symmetric microscopic laws) and weak versions (which can be compatible with time symmetric microscopic laws) are given. This is part of a larger project that aims to explain the arrows as consequences of a common time symmetric principle in the set of all possible universes. However, even if we accept that both arrows may have the same origin, this does not imply that they are equivalent, and it is argued that there can be situations where one arrow may be well-defined but the other is not.

  • 14.
    Åman, Jan E.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bengtsson, Ingemar
    Stockholm University, Faculty of Science, Department of Physics.
    Pidokrajt, Narit
    Thermodynamic Metrics and Black Hole Physics2015In: Entropy, E-ISSN 1099-4300, Vol. 17, no 9, p. 6503-6518Article in journal (Refereed)
    Abstract [en]

    We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular, we analyze its global properties and extend it to take the entropy of the inner horizon into account. A brief discussion of Kerr-Newman black holes is included.

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