The European automotive sector undergoes a severe transformation that is driven by the increasing uptake of alternative drivetrains. In the year 2050 it is expected that 40-80% of new vehicles entering the vehicle stock will be electric (Hill and Bates, 2018). Even though the electrification of the vehicle stock may contribute positively to reaching the EU climate targets, the transformation will also create costs, not only monetary, but also in terms of efforts and losses of functionality. On the one hand substantial efforts will be needed to extract, concentrate and refine materials to produce components and vehicles with new drivetrain technology. On the other hand considerable efforts will be related to restoring functionality losses that result from the large-scale exchange of the vehicle fleet. To assess the effect of the vehicle stock transformation on resource use a dynamic material flow analysis (MFA) is employed and five possible future scenarios of the mobility transition are modelled for the EU until 2050. In a second step the results of the MFA are evaluated through the method of Statistical Entropy Analysis (SEA). The SEA results show that the changes in the vehicle stock, its renewal rate, as well as the adaptation of the reuse, remanufacturing-, and recycling- system, need to be aligned to the pace of the transition to minimize the loss of functionality and reduce the efforts involved. The study demonstrates how SEA can be used to evaluate future socio-technological transitions of larger systems like the European automotive system and identify the best combinations of resource management strategies. It is shown that SEA provides insights that allow to quantify hotspots of functionality loss and determine the most effective combinations of product stock and materials management interventions, contributing to more sustainable use of resources and existing stocks.

In this paper we introduce a type of harmoniums that uses only computations in the domain of information without resorting to probabilities. Starting from the probabilistic description of binary harmoniums---or Restricted Boltzmann Machines (RBMs)---we use the shifted R\'enyi information function to obtain a description of harmoniums, hence called informational harmoniums, in terms of some information semifields recently described where the harmonium architecture is concisely expressed by a matrix whose origin and range spaces of visible inputs and hidden units are semi-vector spaces.
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On the one hand, inference in an informational harmonium is expressed in terms of vector-matrix operations in information semi-vector spaces.
Taking the extreme values of the R\'enyi parameter in the information semifields we obtain the min-plus semifield and the operation of the harmoniums becomes additively-idempotent.
This leads into one of four possible different forms types of Galois connections between the input and output spaces.
In this extreme case, we discuss the representation spaces of the input and hidden nodes of informational harmoniums in terms of a variant of formal concept analysis.
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On the other hand, learning resembles a process akin to hetero-associative morphological memory construction in a non-idempotent semifield, unless again the value of the R\'enyi parameter is extremized. In this situation we derive formulas where negative loglikelihood minimisation of training data are carried out algebraically without resorting to derivatives.

It is well-known that the Fourier equation for heat conduction is not satisfactory in many cases, such as low-temperature situations. It motivated the researchers to find possible extensions. There are numerous approaches in the literature, here we apply non-equilibrium thermodynamics with internal variables.

The first, and successfully applied generalized constitutive equation is called Maxwell-Cattaneo-Vernotte (MCV) equation. It is quite straightforward to derive using the internal variable theory. However, when nonlinear attributes come into the picture, there are some significant consequences that must be investigated further.

In the present paper [1], we are considering temperature-dependent material parameters, e.g., the thermal conductivity and the relaxation time both depend on the temperature. A consistent analysis shows that in some cases, the temperature dependence of mass density follows immediately. It cannot be avoided; thus, the mechanical field has to be introduced to obtain a physically admissible solution.

On the other hand, we investigated the numerical solutions of such a nonlinear MCV equation. We found that the nonlinear numerical stability analysis can be substituted with the linear one by estimating the maximum of the temperature field apriori. Here, we present the effects of temperature dependence and demonstrating the usage of the developed numerical code.

[1] R. Kovács, P. Rogolino: Numerical treatment of nonlinear Fourier and Maxwell-Cattaneo-Vernotte heat transport equations, Accepted in International Journal of Heat and Mass Transfer, 2019. Arxiv: 1910.09175

It is easily seen that the heat-flow statement of 2nd law of thermodynamics is equivalent to information irreversibility when p(x,t) satisfies a general nonlinear 2nd order diffusion equation.
In many situations the viscosity solution of a nonlinear wave equation is that which maintains a specified conservation law and maximizes the entropy jump at a shock.
There are some systems in which information is not monotonic and yet it would be helpful to view entropy as predominantly increasing:
(i) Heat and mass transport in the plasma universe cannot be represented by classical diffusion with unbounded speed of propagation. The simplest phenomenological correction to the hyperbolic diffusion equation is predominantly irreversible.
(ii) A pure quantum state satisfying the Schrödinger equation. By the Hopf-Cole transformation this is equivalent to the momentum equation of the irrotational Madelüng fluid. However interventionist measurement induces vorticity in the fluid, which dissipates along with entropy increase during collapse to an eigen-state. While vorticity is present a full description requires a vector potential as well as the Schrödinger potential.
(iii) So-called fourth-order diffusion is information-irreversible only for an identified class of nonlinear diffusivities.

Initialization of composite quantum systems into highly entangled states is important to enable their use for quantum technologies. However, unavoidable noise in the preparation stage makes the system state mixed, hindering the achievement of this goal. We address this problem in the context of identical particle systems adopting the operational framework of spatially localized operations and classical communication (sLOCC). After a brief description of the formalism, we define the entanglement of formation for an arbitrary state (pure or mixed) of two identical qubits, valid for both bosons and fermions. We then introduce an entropic measure of spatial indistinguishability as an information resource, tunable by the shapes of spatial wave functions. We finally apply these tools to a situation of experimental interest, that is noisy entangled state preparation. We find that spatial indistinguishability, even partial, can be a property shielding nonlocal entanglement from preparation noise, independently of the exact shape of spatial wave functions. These results prove that quantum indistinguishability is an inherent control for noise-free entanglement generation.

Entropy has been, and continues to be, one of the most misunderstood of physical concepts. This is because entropy is a quantification of one’s state of ignorance about a system rather than a quantification of some aspect of a system itself. In this talk I will begin by looking back at the history of entropy tracking the evolution of thought from Carnot’s generalized heat engine, Lord Kelvin’s temperature scale, Clausius’ entropy, to Boltzmann’s counting of microstates. This evolution in thought then took significant leaps as the concept of Shannon’s information was introduced and Jaynes, realizing that this was a matter of inductive inference, introduced the principle of maximum entropy. The concept of entropy continues to evolve as demonstrated by the relation between entropy and the relevance of questions. As a result, the future holds great promise as information-theoretic and entropic methods are justifiably and confidently applied to new problems in new domains far beyond those involving thermodynamics, statistical mechanics and communication theory. And we will see entropic techniques employed in new technologies, such as question-asking machines.

Transport in small-scale biological and soft-matter systems typically occurs under confinement conditions in which particles proceed through obstacles and irregularities of the boundaries that may significantly alter their trajectories. A transport model that assimilates the confinement to the presence of entropic barriers provides an efficient approach to quantify its effect on the particle current and the diffusion coefficient. We review the main peculiarities of entropic transport and treat two cases in which confinement effects play a crucial role, with the appearance of emergent properties. The presence of entropic barriers modifies the mean first-passage time distribution and therefore plays a very important role in ion transport through micro- and nano-channels. The functionality of molecular motors, modeled as Brownian ratchets, is strongly affected when the motor proceeds in a confined medium that may constitute another source of rectification. The interplay between ratchet and entropic rectification gives rise to a wide variety of dynamical behaviors, not observed when the Brownian motor proceeds in an unbounded medium. Entropic transport offers new venues of transport control and particle manipulation and new ways to engineer more efficient devices for transport at the nanoscale.

In nonlinear dynamics, basins of attraction are defined as the set of points that, taken as initial conditions, lead the system to a specific attractor. This notion appears in a broad range of applications where multistability is present, which is a common situation in neuroscience, economy, astronomy, ecology, and other disciplines. Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we call them Wada basins. Usually, Wada basins have been considered even more unpredictable than fractal basins. However, this particular unpredictability has not been fully unveiled until the introduction of the concept of basin entropy. The basin entropy provides a quantitative measure of how unpredictable a basin is. With the help of several paradigmatic dynamical systems, we illustrate how to identify the ingredients that hinder the prediction of the final state. The basin entropy together with two new tests of the Wada property have been applied to some physical systems such as experiments of chaotic scattering of cold atoms, models of shadows of binary black holes, and classical and relativistic chaotic scattering associated to the Hénon-Heiles Hamiltonian system in astrophysics.

[1] A. Daza, et al. Scientific Reports 5, 16579 (2015)

[2] A. Daza, et al. CNSNS 43, 220–226 (2017)

[3] A. Daza, et al. Scientific Reports 6, 31416 (2016)

[4] A. Daza, et al. Phys. Rev. A 95, 013629 (2017)

[5] A. Daza, et al. Mark Edelman, Elbert Macau and Miguel A. F. Sanjuán, Editors. Springer, Cham, 2018

[6] Alvar Daza, et al. Phys. Rev. D 98, 084050 (2018)

[7] A. Daza, et al. Scientific Reports 8, 9954 (2018)

[8] A. Wagemakers, et al. CNSNS 84, 105167 (2020)

In the first part of my lecture, I will review information-geometric structures and highlight the important role of divergences. I will present a novel approach to canonical divergences which extends the classical definition and recovers, in particular, the well-known Kullback-Leibler divergence and its relation to the Fisher-Rao metric and the Amari-Chentsov tensor.

Divergences also play an important role within a geometric approach to complexity. This approach is based on the general understanding that the complexity of a system can be quantified as the extent to which it is more than the sum of its parts. In the second part of my lecture, I will motivate this approach and review corresponding work.

References:

1. N. Ay, S.I. Amari. A Novel Approach to Canonical Divergences within Information Geometry. Entropy (2015) 17: 8111-8129. doi:10.3390/e17127866.

2. N. Ay, J. Jost, H. V. Le, L. Schwachhöfer. Information geometry. Ergebnisse der Mathematik und Ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics, Springer 2017.

3. N. Ay. Information Geometry on Complexity and Stochastic Interaction. Entropy (2015) 17(4): 2432-2458. doi: 10.3390/e17042432.

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. Gravity's Rainbow seems to offer a different scheme which is able to remove infinities when Black Hole Entropy is computed in contrast to what happens in conventional approaches. In particular, we apply the Gravity's Rainbow regularization scheme to the computation of the entropy of a Schwarzschild black hole from one side. In a second step, we will consider the effects of rotations on the calculation of some thermodynamical quantities like the free energy, internal energy and entropy. Even in this case, in ordinary gravity, when we evaluate the density of states of a scalar field close to a black hole horizon, we obtain a divergent result which can be kept under control with the help of some standard regularization and renormalization processes. Once again we will show that when we use the Gravity's Rainbow approach such regularization/renormalization processes can be avoided. A comparison between the calculation done in an inertial frame and in a comoving frame is presented.