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Rényi Entropy in Statistical Mechanics Fuentes, Jesús ; Goncalves, Jorge in Entropy (2022), 24(8), 1080 Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to ... [more ▼] Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy and instead tending to introduce it artificially. However, as we will show, modifications to the theory of statistical mechanics are needless to see how Rényi entropy automatically arises as the average rate of change of free energy over an ensemble at different temperatures. Moreover, this notion is extended by considering distributions for isospectral, non-isothermal processes, resulting in relative versions of free energy, in which the Kullback–Leibler divergence or the relative version of Rényi entropy appear within the structure of the corrections to free energy. These generalisa- tions of free energy recover the ordinary thermodynamic potential whenever isothermal processes are considered. [less ▲] Detailed reference viewed: 10 (1 UL)Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production ; Fodor, Etienne ; et al in Entropy (2022) Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained ... [more ▼] Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself. [less ▲] Detailed reference viewed: 18 (0 UL)Exploring Spillover Effects for COVID-19 Cascade Prediction ; Chen, Xihui ; Zhong, Zhiqiang et al in Entropy (2022), 24(2), Detailed reference viewed: 45 (3 UL)Limits to Perception by Quantum Monitoring with Finite Efficiency ; Del Campo Echevarria, Adolfo in Entropy (2021) We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds ... [more ▼] We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent's perception of the system is altered by access to additional information We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain. [less ▲] Detailed reference viewed: 25 (0 UL)Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions di Cairano, Loris ; Gori, Matteo ; in Entropy (2021), 23(11), Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical ... [more ▼] Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy [less ▲] Detailed reference viewed: 64 (1 UL)Design of a 2-Bit Neural Network Quantizer for Laplacian Source ; ; et al in Entropy (2021), 23(8), 933 Achieving real-time inference is one of the major issues in contemporary neural network applications, as complex algorithms are frequently being deployed to mobile devices that have constrained storage ... [more ▼] Achieving real-time inference is one of the major issues in contemporary neural network applications, as complex algorithms are frequently being deployed to mobile devices that have constrained storage and computing power. Moving from a full-precision neural network model to a lower representation by applying quantization techniques is a popular approach to facilitate this issue. Here, we analyze in detail and design a 2-bit uniform quantization model for Laplacian source due to its significance in terms of implementation simplicity, which further leads to a shorter processing time and faster inference. The results show that it is possible to achieve high classification accuracy (more than 96% in the case of MLP and more than 98% in the case of CNN) by implementing the proposed model, which is competitive to the performance of the other quantization solutions with almost optimal precision. [less ▲] Detailed reference viewed: 51 (1 UL)A Survey of Information Entropy Metrics for Complex Networks Omar, Yamila ; Plapper, Peter in Entropy (2020) Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it ... [more ▼] Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts. [less ▲] Detailed reference viewed: 66 (5 UL)Thermodynamics of Majority-Logic Decoding in Information Erasure ; Herpich, Tim ; et al in Entropy (2019), 21(3), 284 Detailed reference viewed: 188 (6 UL)Detailed Fluctuation Theorems: A Unifying Perspective ; Esposito, Massimiliano in Entropy (2018) We present a general method to identify an arbitrary number of fluctuating quantities which satisfy a detailed fluctuation theorem for all times within the framework of time-inhomogeneous Markovian jump ... [more ▼] We present a general method to identify an arbitrary number of fluctuating quantities which satisfy a detailed fluctuation theorem for all times within the framework of time-inhomogeneous Markovian jump processes. In doing so, we provide a unified perspective on many fluctuation theorems derived in the literature. By complementing the stochastic dynamics with a thermodynamic structure (i.e., using stochastic thermodynamics), we also express these fluctuating quantities in terms of physical observables. [less ▲] Detailed reference viewed: 254 (2 UL)Detailed Fluctuation Theorems: A Unifying Perspective ; Esposito, Massimiliano in Entropy (2018), 20(9), Detailed reference viewed: 52 (0 UL)Quantum Thermodynamics with Degenerate Eigenstate Coherences ; Esposito, Massimiliano ; in Entropy (2016), 18(12), Detailed reference viewed: 70 (1 UL)Quantum Thermodynamics with Degenerate Eigenstate Coherences Bulnes Cuetara, Gregory ; Esposito, Massimiliano ; in Entropy (2016), 18(447), We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a ... [more ▼] We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a finite-time fluctuation theorem for mechanical work and energy and matter currents. Using a double quantum dot junction model, local eigenbasis coherences are shown to play a crucial role on thermodynamics and on the electron counting statistics. [less ▲] Detailed reference viewed: 176 (6 UL)Fact-Checking Ziegler’s Maximum Entropy Production Principle beyond the Linear Regime and towards Steady States Polettini, Matteo in Entropy (2013), 15(7), 2570-2584 We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in ... [more ▼] We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to maximize entropy production as the system approaches the steady state. In particular: (1) we show that Ziegler’s principle of thermodynamic orthogonality leads to stringent reciprocal relations for higher order response coefficients, and in the framework of stochastic thermodynamics, we exhibit a simple explicit model that does not satisfy them; (2) on a network, enforcing Kirchhoff’s current law, we show that maximization of the entropy production prescribes reciprocal relations between coarse-grained observables, but is not responsible for the onset of the steady state, which is, rather, due to the minimum entropy production principle. [less ▲] Detailed reference viewed: 160 (3 UL) |
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