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** Arieh Ben-Naim**

*Department of Physical Chemistry, The Hebrew University of Jerusalem**, Jerusalem, Israel*

**Entropy and Information Theory: Uses and Misuses**

Before discussing the uses and misused of entropy and information theory we will first review the definitions of entropy. We present three different, but equivalent definitions of entropy: Clausius’s and Boltzmann’s definitions, and the new definition based on Shannon’s measure of information (SMI). Once we have clear-cut definitions of entropy and the SMI, we shall discuss their different ranges of applicability, or what Einstein called the** framework of applicability of thermodynamics**. We shall see that nothing in the definition of entropy indicate any kind dependence on time. Therefore, we can conclude that entropy is a timeless quantity. Furthermore, we examine the possibility of defining entropy for non-equilibrium state. We find that while the SMI may be defined for any probability distribution, including non-equilibrium distributions, entropy is defined only for

**. Therefore, entropy may not be used for any living system, and not for the entire universe. We conclude that over the years, the boundaries of applicability of entropy, the Second Law and SMI were breached.**

*equilibrium distributions*References:

- Ben-Naim, A. (2017),
*Information Theory*, World Scientific, Singapore - Ben-Naim, A. (2018),
*Time’s Arrow. The Timeless Nature of Entropy and the Second Law*, Lulu Publication

**Przemysław Chełminiak**

*Faculty of Physics, Adam Mickiewicz University, Poznań, Poland*

*Biological molecular machines can process information to reduce energy losses*

Biological molecular machines are enzymes that simultaneously catalyze two processes, one donating free energy and second accepting it. Recent studies show that most native protein enzymes have a rich stochastic dynamics that often manifests in fluctuating rates of the calatyzed processes and the presence of short-term memory resulting from transient non-ergodicity. For such dynamics, we prove the generalized fluctuation theorem predicting a possible reduction of energy dissipation at the expence of creating some information stored in memory. The theoretical relationships are verified in computer simulations of random walk on a model critical complex network. The transient utilization of memory turns out to be crucial for the movement of protein motors and the reason for most protein machines to operate as dimers or higher organized assemblies. Our conclusions are based on analysis of the simulated time course of the catalyzed processes expressed by the strings of discrete jumps at random moments of time. Since similar signals can be registered in the experiments, all the theses of our studies are open for experimental verification.

**Dariusz Chruściński**

*Institute of Physics, Nicolaus Copernicus University, Toruń, Poland*

*Information flow versus divisibility for qubit evolution*

The relation between lack of information backflow and completely positive divisibility for noninvertible qubit dynamical maps is analyzed. Recently, these two concepts were shown to be fully equivalent for the so-called image nonincreasing dynamical maps. Here we show that this equivalence is universal for any qubit dynamical map. Our analysis is illustrated by several examples of qubit evolution, including dynamical maps which are not image nonincreasing.

**Krzysztof Domino, Agnieszka A. Tomaka**

*Institute of Theoretical and Applied Informatics, Polish Academy of **Sciences, Gliwice, Poland*

**Investigation of information tied to higher order cross-correlation of multivariate data**

We discuss such statistical dependency of multivariate data (signals) that are not included in the correlation matrix (used in a standard statistical dependency analysis). This (higher order) dependency appear if data follow other than normal (Gaussian) probabilistic model. We present mathematical, informative and statistical approach to the problem. For the real life data application we analyse signals acquired from probes placed symmetrically on both sides of the patient’s face, and demonstrate the asymmetry of the mandible movement.

*Adam Gadomski ^{1}, Marcin Kośmieja^{2,3}, Piotr Bełdowski^{1}, Natalia Kruszewska^{1}, Piotr Weber^{4}, and Jacek Siódmiak^{1}*

^{1}Institute of Mathematics and Physics, UTP University of Science and Technology, Bydgoszcz, Poland^{2}Faculty of Telecommunications, Computer Science and Electrical Engineering, UTP University of Science and Technology, Bydgoszcz, Poland^{3}Nokia Solutions and Networks Sp. z o.o., Warszawa, Poland^{4}Atomic and Optical Physics Division, Department of Atomic, Molecular and Optical Physics, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gdańsk, Poland

*Interpreting the aggregation outcomes in entropy-production biomolecular systems*

Aggregation of biomolecular matter stands for one of fromidable tasks to be addressed in order to help resolve human health problems such as neurodegenerative diseases or obstructed locomotion.

On the one hand, there are computer simulation experiments that help a great deal to shed more light on decisive peculiarities of biomolecular aggregations, expressing their basic constituents in a form of granules that appear at the expense of a few thermal kT units of the energy put in the system, or alike [1].

On the other hand, the mesoscopic nonequilibrium thermodynamics, addressing readily the aggregations, works well close to thermodynamic equilibrium. The crucial thing is that for slowly evolving subdiffusive systems a local equilibrium is sometimes equally slowly approachable by the system. As a consequence, the interpretation of the results obtained from the simulations ought to be complemented by the fractional time operators that are able to detect the main trend of the approach examined, while based on modified (Shannon) entropy production, proportional to the product of the respective thermodynamic forces and fluxes [2,3].

In the approach only a fractional-operator including modification of the flux [2] when system enters the subdiffusive domain is considered and discussed.

- P. Bełdowski, P. Weber, A. Dedinaite, P. Claesson, A. Gadomski, „Physical crosslinking of hyaluronic acid in the presence of phospholipids in an aqueous nano-environment”, Soft Matter 14/44 (2018), 8997-9004.
- P. Weber, P. Bełdowski, M. Bier, A. Gadomski, „Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment”, Entropy 20/9 (2018), 651-655.
- A. Gadomski, N. Kruszewska, P. Bełdowski, „Temperature dependent volume expansion of microgel in nonequilibria”, Eur. Phys. J. B 91 (2018), 237-243.

*Bartłomiej Gardas*

*Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Kraków, Poland*

**Parallel in time dynamics with quantum annealers**

Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. In particular, quantum annealers. Although quantum supremacy has not been established thus far, there exist a plethora of algorithms promising to outperform classical computers in the near-term future. Here, we propose a parallel in time approach to simulate dynamical systems designed to be executed already on present-day quantum annealers. In essence, purely classical methods for solving dynamics systems are serial. Therefore, their parallelization is substantially limited. In our approach, however, the time evolution is rephrased as a ground–state search of a classical Ising model. A task solved intrinsically in parallel by quantum computers. Our idea is exemplified by simulating the Rabi oscillations generated by a two-level system (qubit) experimentally.

**Jerzy Górecki**

*Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland*

*Applications of information theory methods for evolutionary optimization of chemical computers*

It is commonly believed that information processing in living organisms is based on chemical reactions. However, human attempts to construct chemical information processing devices demonstrate that it is difficult to design them using the bottom-up strategy. In my lecture I discuss the alternative top-down strategy. The parameters of a network of chemical oscillators are optimized to perform required function with the maximum accuracy. I concentrate on chemical database classifiers and discuss how information theory methods can be applied to obtain the best structure of the network [1,2].

- K. Giżyński, J. Górecki; A Chemical System that Recognizes the Shape of a Sphere, CMST 22(4) 167-177 (2016), DOI:10.12921/cmst.2016.0000057
- K. Giżyński, J. Górecki; Cancer classification with a network of chemical oscillators, Phys.Chem.Chem.Phys., 19, 28808 (2017), DOI: 10.1039/c7cp05655a

**Janusz A. Hołyst ^{1,2}, Robert Paluch^{1}, Łukasz Gajewski^{1}, Krzysztof Suchecki^{1}, Xiaoyan Lu^{3}, Boleslaw K. Szymański^{3}**

^{1}Center of Excellence for Complex Systems Research, Faculty of Physics, *Warsaw University of Technology, Warsaw, Poland *^{2}ITMO University, Saint Petersburg, Russia^{3}Rensselaer Polytechnic Institute, Troy, NY, USA

**Detection of information source in complex networks**

Spread over complex networks is a ubiquitous process with increasingly wide applications. Locating spread sources is often important, e.g. finding the patient one in epidemics, or source of rumor spreading in social network. Here we explore the problem of complexity of currently known methods as well as we investigate the validity of the assumption that information spreads only via the shortest paths. Pinto, Thiran and Vetterli [1] introduced an algorithm (PTVA) to solve the problem of source detection in which a limited set of nodes act as observers and report times at which the spread reached them. PTVA uses all observers to find a solution and assumes the information travels via a single, shortest path, which by assumption is the fastest way. Here we propose a new approach [2] in which observers with low quality information (i.e. with large spread encounter times) are ignored and potential sources are selected based on the likelihood gradient from high quality observers. The original complexity of PTVA is O(N^a), where 3 <a <4) depends on the network topology and number of observers (N denotes the number of nodes in the network). Our Gradient Maximum Likelihood Algorithm (GMLA) reduces this complexity to O(N^2 log(N)) without reduction of the detection accuracy.

We also show that assumption that information spreads only via the shortest paths leads to the overestimation of propagation time for synthetic and real networks, where multiple shortest paths as well as longer paths between vertices exist [3]. We propose a new method of source estimation based on maximum likelihood principle, that takes into account existence multiple shortest paths. It shows up to 1.6 times higher accuracy in synthetic and real networks.

- Pinto PC, Thiran P, Vetterli M. Locating the source of diffusion in large-scale networks. Physical Review Letters. 2012;109:1–5. doi: 10.1103/PhysRevLett.109.068702
- Paluch, R., Lu, X., Suchecki, K., Szymański, & B. K., Hołyst, J. A. (2018) Fast and accurate detection of spread source in large complex networks. Scientific Reports, 8, 2508
- Gajewski, L. G., Suchecki, K., Hołyst, J. A. (2019) Multiple propagation paths enhance locating the source of diffusion in complex networks. Physica A, 519, 34

*Michał Horodecki*

*International Centre for Theory of Quantum Technologies, University of Gdańsk, Gdańsk, Poland*

*Resource approach to thermodynamics*

We shall review an approach to thermodynamics that resembles resource theoretic approach in quantum entanglement theory or quantum information theory. It involves basic class of operations called Thermal Operations. The main problem is to determine possible transitions between two states of the system by means of Thermal Operations. I will present solution for systems diagonal in energy eigenbasis as well as partial solution for systems posesing coherences. I will also analyse to what extent performing Thermal Operations is Markovian. Heat engines will be also considered within the above paradigm.

*Rajendrasinh Jadeja, Shobhit K. Patel, Juveriya Parmar, Shreyas Charola*

*Marwadi University, Rajkot, India*

**Efficient graphene solar absorber**

Efficiency is a very important part while designing any solar absorber. Graphene is a carbon allotrope with excellent electrical and optical properties. These properties of graphene can be combined with solar absorber to increase their efficiency. Transparency and flexibility are the other two important parameters of graphene which can be combined with solar cells to make them transparent and flexible. Graphene also gives the tuning capability to the solar absorber. The efficient graphene solar absorbers are applicable in designing energy harvesting devices.

*Karol Karpiński, Sylwia Zielińska – Raczyńska,* David Ziemkiewicz

*Institute of Matemathics and Physics, UTP University of Science and Technology, Bydgoszcz, Poland*

**Surface plasmons on fractal structures**

Fractal geometries are characterized by many unique properties, among which the most striking one is their non-integer dimension. We numerically study how the surface-plasmon polaritons propagate through these peculiar structures, producing transmission and reflection spectra which are also fractals. It has been shown that the fractal dimension is directly linked to the Shannon (information) entropy [1]. Therefore, our study may provide a new insights in the field of information processing in plasmonic systems.

- O. Zmeskal, P. Dzik, M. Vesely,
*Computers and Mathematics with Applications*66, 135–146 (2013).

*Jerzy Łuczka*

*Institute of Physics, University of Silesia, Katowice, Poland*

*Quantum teleportation: still fantasy or now reality*

In the lecture I will introduce fundamentals of quantum teleportation. To this aim two elements are needed: quantum physics + information transmitted by classical communication. I say about teleportation protocols and present experimental realizations.

*Danuta Makowiec*

*Institute of Theoretical Physics and Astrophysics, Gdansk University, Gdańsk, Poland*

*Machine learning methods in obtaining new information about old problems: estimates of healthy people’s heart rate variability*

Enormous progress in machine learning achievements, going together with their excellent implementations on user-friendly platforms, have pushed many of us towards this methodology. Can we get a better explanation of the data under study with these new tools? Or maybe these methods provide answers to our questions in a fast and simple way? In the following we show our practice with data formed from ECG recordings on healthy people of different age. The problem is how the age affects the normal rhythm of a healthy heart. The human heart is under the constant influence of the autonomic nervous system (ANS). Therefore, heart rate variability has been proposed as an indicator of regulatory function of ANS. Separation of different patient groups based on heart rate variability parameters is an old problem that still has no satisfactory solution.

*Łukasz Rudnicki*

*The International Centre for Theory of Quantum Technologies, Gdańsk University, Gdańsk, Poland*

**Uncertainty-reality complementarity and entropic uncertainty relations ****with quantum memory**

Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified by means of entropic measures. However in certain systems all observables are real so there is no state-independent ‘reality trade-off’ between non-commuting observables. We explain in which way the entropic uncertainty relation in the presence of quantum memory perfectly supplements the discussed notion of reality, rendering trade-offs between reality and quantum uncertainty.

*Nikolay K. Vitanov, Roumen Borisov*

*Institute of Mechanics, Bulgarian Academy of Sciences,** Sofia, Bulgaria*

**Statistical features of a model of motion of substance in channels of networks**

We consider a channel constructed by nodes of a network connected by edges (ways) that allow a motion of substance between the nodes of the channel. We study this motion for the case of a channel that consists of a main (primary) arm and a system of arms splitting from the primary arm or from some of the secondary arms of the channel. The motion of substance is connected to statistical distributions for the amounts of substance in the nodes of the channel. Many of the obtained distributions are long-tail ones. We describe some of the distributions and discuss several of their characteristics.

*Krzysztof W. Wojciechowski*

*Institute of Molecular Physics, Polish Academy of Sciences, Poznań, Poland*

**Entropy driven effects in some simple planar models**

In hard body models, i.e. model systems composed of particles interacting through hard potential – infinite when any two particles overlap and zero otherwise, all accessible configurations have the same, zero energy. Hence, at a given density, thermodynamic properties of such models are determined by the (configurational) entropy alone. Despite their simplicity, the hard body models are nontrivial and play a crucial role in understanding physical properties of various real (e.g. condensed matter) systems. This is because the hard potential is the simplest one which well reproduces the excluded volume effects caused by the cores of real molecules.

In this lecture, some surprising phenomena observed in some hard body models: (A) consisted of molecules composed of touching hard discs, and called hard cyclic multimers, and (B) consisted of eqilateral triangles, squares and rectangles, are discussed. In particular, (1) negative Poisson’s ratio observed in systems of hard cyclic septamers, hexamers, tetramers and trimers, (2) transition from 5-fold to 6-fold symmetry patterns in cyclic pentamers as well as (3) phase separation of triangles and squares, are presented. Finally, (4) observation of the freezing of dimers into an aperiodic solid phase, which reveals the crucial role of the degeneracy entropy in this phase transition, is discussed in detail.

**David Ziemkiewicz, Sylwia Zielińska – Raczyńska**

*Institute of Matemathics and Physics, UTP University of Science and Technology, Bydgoszcz, Poland*

**Quantum information processing with Rydberg excitons**

Efficient and precise realization of high-quality quantum coherence effects in semiconductor is of a great importance for quantum engineering and information processing. We show that one can take advantage of Rydberg excitons to realize such a tool [1,2]. The unique combination of their huge size, long radiative lifetimes, possible strong dipole-dipole interaction and miniaturization of samples can be exploited to perform robust light-exciton quantum interfaces for quantum information processing purposes.

- S. Zielińska – Raczyńska, David Ziemkiewicz, and Gerard Czajkowski,
*Phys. Rev. B*94, 045205 (2016). - S. Zielińska – Raczyńska, David Ziemkiewicz, and Gerard Czajkowski,
*Phys. Rev. B*95, 075204 (2017).

*Marek Żukowski*

*The International Centre for Theory of Quantum Technologies, Gdańsk University, Gdańsk, Poland*

*Quantum advantage in communication complexity **problems.*

Quantum correlations which violate Bell inequalities can be related with reduction of information transfer (communication complexity) in computational problems involving several partners, none of whom has full data to solve a certain computational task. How general is this relation? Can one see the quantum advantage in real experiments? Do we need entanglement to gain the advantage? Past crucial results will be presented, and surprising recent twists in out attempts to understand all that.