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  • 61 Reads
On the relation of Eckart and Landau-Lifshitz reference frames for higher orders in the dissipative fluxes couplings

In the kinetic description of a relativistic gas, macroscopic quantities are usually studied either in the reference frame that moves with the fluid (the so-called Eckart frame) or in the frame where there is no energy dissipation flux (Landau Lifshitz frame). In a closer and detailed view, the Landau Lifshitz reference frame requires several approximations to relate it with the Eckart’s or particle frame. For the energy-momentum tensor not contain energy fluxes is necessary to neglect couplings among dissipative flows. It is well known that at first order particle 4-flux contains a dissipative term related to the heat flux and also defines a Lorentz reference frame through a timelike vector. In this work, we relate these reference frames up to higher orders in dissipative fluxes couplings and compare the properties of the corresponding systems of transport equations in both frames emphasizing the entropy balance and its consistency with the second law.

  • Open access
  • 64 Reads
Nonlinear dynamical screening effects and strong local fluctuations of drag forces in collective scattering of particle streams on impurity ensembles

We study the effects of nonequilibrium correlations and interactions between constituent particles of a bunch or pulsed beam, arising in course of its motion through a medium, or under the scattering of particle stream on a cluster or finite cloud of impurities [1]. Formally, these correlations are determined by the effect of dynamical screening. Such induced correlations and dynamical friction forces on impurities are manifested most pronouncedly in the case of collective dynamical screening effect and are enhanced in the case of a nonlinear medium when strong local fluctuations of scattered field begin to act as additional scattering elements along with impurities. In addition, collective scattering effects depend on the degree of impurity cluster disorder [2]. We focus on effects provoked by the collective scattering on randomly inhomogeneous structures and by the presence of local fluctuations. The presence of strong fluctuations of the scattered field is shown to give rise to strong local fluctuations of nonequilibrium forces acting on certain particles within the impurity cluster that can be a precursor of dynamical instability of the cluster, which is manifested in the peculiar behavior of the tails of probability distribution function for the drag force [3]. The description of the impurity cluster in terms of effective parameters breaks down due to the presence of such fluctuations.

Acknowledgments: This work was partially supported by a grant for research groups of young scientists from the National Academy of Science of Ukraine (Project No. 0120U100155).

[1] O.V. Kliushnychenko and S.P. Lukyanets, Effects of gas interparticle interaction on dissipative wake-mediated forces, Phys. Rev. E 95, 012150 (2017).
[2] O.V. Kliushnychenko and S.P. Lukyanets, Effects of collectively induced scattering of gas stream by impurity ensembles: Shock-wave enhancement and disorder-stimulated nonlinear screening, Phys. Rev. E 98, 020101(R) (2018).
[3] O.V. Kliushnichenko, S.P. Lukyanets, arXiv: 2012.09266 (2020).

  • Open access
  • 29 Reads
Breaking of ensemble equivalence in networks

It is generally believed that, for physical systems in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature, the original argument being that in the canonical ensemble at fixed temperature the energy fluctuations are negligible with respect to the average energy. Today, most textbooks in statistical physics still convey the message that the equivalence of ensembles holds universally for every physical system; however, various examples have been identified for which the microcanonical and canonical ensembles are not equivalent (e.g. for certain many-body systems encountered in models of fluid turbulence, quantum phase separation, etc.).

Here we show that ensemble nonequivalence can manifest itself also in discrete enumeration problems. We argue that, for any enumeration problem where we need to count microcanonical configurations compatible with a given constraint, there exists a dual problem involving canonical configurations induced by the same constraint. We then prove a general result showing that, for discrete systems, ensemble equivalence reduces to equivalence of the large deviation properties of microcanonical and canonical probabilities of a single microstate. As specific examples, we consider ensembles of networks with topological constraints. We find that, while graphs with a given number of links are ensemble-equivalent, graphs with a given degree sequence (including random regular graphs, sparse scale-free networks, and core-periphery networks) are not. We also find that, as the heterogeneity of the degree distribution increases, the violation of non-equivalence gets more severe.

Our proof of the breakdown of ensemble equivalence in graphs with given degree sequence provides a theoretical explanation for some recent observations, namely the fact that the canonical and microcanonical entropies of random regular graphs are different even in the thermodynamic limit and the non-vanishing of canonical fluctuations in the configuration model.

  • Open access
  • 84 Reads
Entropy and entropic forces to model biological fluids

Biological systems tend to exhibit common organizational patterns despite they diversity and different spatial and temporal scales. Living cells are complex systems that may be characterized by fluids crowded by hundreds of different elements in particular by a high density of polymers; they are an excellent and challenging laboratory to study exotic emerging physical phenomena where entropic forces emerge from organization processes of many-body interactions. There may be many entropic forces emerging in a biological fluid but most of them are consequences or can be reduced to the crowding and exclusion volume effects. Since entropic forces are emergent phenomena resulting from the tendency of a thermodynamic system to maximize its entropy, the macroscopic variables describing the system tend to evolve from one state to another state that is statistically more probable. If an external force exerted on the system point in the direction of decreasing its entropy while the entropic forces generated by the system point in the direction of increasing its entropy, when the system reaches its maximum entropy, the entropic force becomes zero. Therefore, the competition between entropic and physical forces may generate complex behaviors like phase transitions that living cells may use to accomplish their functions. In the era of the big data, when biological information abounds but general principles and precise understanding of the microscopic interactions scarce, the entropy methods may offer significant information including statements of the physical interactions between the diversity of constituent elements, inferred only from experimental data. In this work we develop a model of a biological fluid involving the competition of entropic and physical forces that living cells seem to use to accomplish their functions as has been recently started to be understood. The target audience for this article are interdisciplinary researchers in complex systems, particularly in biophysics modeling.

  • Open access
  • 63 Reads
Investigating the structure-dynamics-function relationship in antibodies

The paradigm that connects sequence, structure and function in proteins has been revisited in recent years, opening new perspectives on the importance of dynamics [1]. In this work we tackle this issue through the analysis of all-atom molecular dynamics (MD) simulations, with the final objective of correlating motions and structural features. We first characterize the dynamics of an antibody, through 2 μs of all-atom molecular dynamics simulations, to investigate the correlation between structural features and the flexibility of the molecule. Subsequently we perform 2 μs of all-atom MD simulations of the same antibody bound to its antigen, to investigate the changes in dynamics.

We analyzed the simulations through various different techniques among which we highlight the power of those based on the calculation of the information transfer between different amino acids [3]. These types of measurements allow us to identify significant correlations among protein regions, providing clues on the mechanism of protein function. The investigations carried out in this work also serve as a guide in the identification of those structural patterns whose preservation is necessary in the construction of coarse-grained models. Overall this study is meant as a starting point for the application of a multi-scale method to biologically relevant macromolecules.

[1] Hensen, U. et al. (2012). Exploring protein dynamics space: the dynasome as the missing link between protein structure and function. PloS one, 7(5).
[2] Scapin, G. et al. (2015). Structure of full-length human anti-PD1 therapeutic IgG4 antibody pembrolizumab. Nat Struct Mol Biol, 22(12):953-8.
[3] Bowerman, S., and J. Wereszczynski. (2016) Detecting Allosteric Networks Using Molecular Dynamics Simulation. Methods in enzymology. 578. 429-47.

  • Open access
  • 43 Reads
Measurement and minimisation of the Mapping Entropy of a Coarse-Grained biomolecular system

All-atom Molecular Dynamics (MD) is the standard approach to perform in silico simulations of biomolecular systems. Despite its central role in modern computational biophysics, MD cannot span the time scales where the majority of relevant biological processes take place. An alternative is represented by coarse-grained (CG) modelling [1], that is, those lower-resolution representations of the system which aim at effectively reducing the number of degrees of freedom of a biomolecule in order to reach previously inaccessible time scales. Among the several statistical mechanics-based CG’ing techniques, we focused on those that measure the difference in information content between the coarse-grained and the all-atom system. We developed a protocol [2] able to compute the Mapping Entropy, which quantifies the amount of information retained upon the process of CG’ing due only to the choice of the Mapping. Our approach can therefore provide the user with the subset of sites which are maximally informative about the original, fully atomistic system. Tests conducted over a set of well-known proteins showed that regions retained with high probability are often related to the biological function of the molecule.

[1] William George Noid. Perspective: Coarse-grained models for biomolecular systems. The Journal of chemical physics, 139(9):09B201 1, 2013.
[2] Marco Giulini, Roberto Menichetti, M Scott Shell, and Raffaello Potestio. An information-theory-based approach for optimal model reduction of biomolecules. Journal of chemical theory and computation, 16(11):6795–6813, 2020.

  • Open access
  • 73 Reads
Complexity inside and outside the brain: how to manage internal (interoceptive) and external (domotics) environment during adaptive inter-actions

Previous studies supported the notion that brain activity is slightly sub-critical in normal waking consciousness (Priesemann et al., 2013), and in this way, it can exert better control over the rest of the world, most of which is critical. This control may take the form of managing endogenous processes within the brain or interacting with the environment in order to functionally shape it (Carhart-Harris et al., 2014). The relationship between complex systems, i.e. human-to-environment relation, from an adaptive perspective is mediated by the sensory system with the main goal of maintaining a balance, aiming for harmony and avoiding ruptures. Through the description of two pilot studies, the advantages of adopting neuroscientific tools for exploring neurophysiological brain-and-body activity during complex inter-actions will be elucidated. This research has been conducted in two different fields of application: the first one investigated how the person answer to a complex domotic environment; the second one regards the deepening of interoceptive awareness as a possible factor influencing functional empathic response to external challenge. In the first study, some distinguishing effects of domotics on users’ cognitive and emotional behavior are highlighted by using the neuroscientific approach. In order to define effects of Smart Home System (SHS) on UX, a neuroscientific wireless multi-methodology was adopted with the purpose of recording and confronting the neural activity (Electroencephalography, EEG) and autonomic system responses (with Biofeedback) of 19 individuals during a resting state (RS) baseline and the exploration of 5 different tech-interaction areas in a domotic environment. In the second study, a BIO-EEG-fNIRS (functional Near Infrared Spectroscopy) co-registration approach was adopted while 20 healthy participants performed a new paradigm for investigating the effects of interoceptive ability on empathy. Overall, the advantages and limitations of the applications of neuroscientific paradigms and tools for analyzing human interaction with complex systems will be discussed.

  • Open access
  • 91 Reads
Complexity as cardiorespiratory coupling measure in neonates with different gestational ages

After the transition from fetal to neonatal life, the cardio-respiratory system needs to adapt to the extrauterine condition. Both the cardiac and respiratory systems display complex dynamics. This study aimed to investigate the relationship between cardiorespiratory coupling, heart rate variability (HRV), and respiration of neonatal with gestational age (GA). Several complexity measures have been developed to quantify the complexity of physiological signals. In this study, we applied sample entropy (SampEn) and the bzip2 compressor to the time series. The mutual information (MI) and the normalized compression distance (NCD) were used to quantify the complexity of the cardiorespiratory coupling.

We analyzed a dataset composed of 30-minutes traces of RR intervals and respiration signals, acquired in the first two days of life, for 33 neonates with GA between 27 and 41 weeks. Of these 33 neonates, 22 babies were premature (<37 weeks), and 4 babies were considered extremely premature (<28 weeks). The Pearson correlation was computed to assess the association between complexity measures and GA.

Results obtained show that for the respiratory signals, SampEn increases as GA increases (r=0.46, p=0.008). However, the SampEn for RR intervals and MI gave non-significant correlations. When we applied the bzip2 compressor to the RR signals, we obtained a positive correlation with GA (r=0.69, p<0.001), but there is no significant correlation between bzip2 of respiratory signals and GA. For the complexity of cardiorespiratory coupling with NCD, we obtained a negative correlation with GA (r=-0.74, p<0.001).

We infer that SampEn presents better results for respiratory signals. However, bzip2 is better when using RR signals. While the complexity of the time series increases with GA, the complexity of the coupling decreases. This finding might emerge from the fact that the heart rate is highly modulated by respiration in premature babies. Future studies should investigate the complementary of these complexity measures.

  • Open access
  • 86 Reads
Entropy-driven Phase Transition of Semiflexible Hard-Sphere Polymer Packings in Two and Three Dimensions

We study, at the atomic level, the behaviour of athermal, linear semiflexible polymers of tangent spheres in thin films of one-layer thickness (2-D systems) and bulk 3-D systems. We employ extensive Monte Carlo simulations [1] at progressively increased concentrations adopting the hard-sphere model to represent interactions between monomers. Extreme, plate-like confinement for thin films is realized through the presence of flat, parallel walls in one dimension with the inter-wall distance being equal to the diameter of the spherical monomers. Chain stiffness is controlled by a tuneable potential for the bending angles whose intensity dictates the rigidity of the polymer backbone. At very high values of bending intensity, the polymer model approaches that of freely-rotated chains and bending angles sample the whole range from acute to obtuse angles, reaching the limit of rod-like polymers. We study how packing density, chain length and stiffness affect the entropy-driven phase transition from initially disordered (random) to ordered (crystal) local and global structures in dense polymer packings in 2-D and 3-D systems and compare against fully flexible chains and monomeric counterparts [2]. To gauge local order, we employ the characteristic crystallographic element (CCE) norm, a descriptor, which can detect and quantify, with high precision, similarity to reference crystals in general atomic and particulate systems [3,4]. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies.

[1] P. Ramos, N. C. Karayiannis and M. Laso, J. Comput. Phys. 375, 918 (2018).

[2] N. C. Karayiannis, K. Foteinopoulou and M. Laso, Int. J. Mol. Sci. 14, 332 (2013).

[3] N. C. Karayiannis, K. Foteinopoulou and M. Laso, J. Chem. Phys. 130, 074704 (2009).

[4] P. Ramos, M. Herranz, K. Foteinopoulou, N. C. Karayiannis and M. Laso, Crystals 10, 1008 (2020).

  • Open access
  • 47 Reads
Chaotic and thermodynamic interplay in nanocavities

Molecular confinement in nanocavity networks implies interplay between thermodynamic and chaotic response leading to surface entropic variations. Molecules, especially water molecules near surfaces are successively trapped and escape from nanocavities [1]. The time scale of physical interactions inside the nanocavities is governed by the molecular mean escape time from the nanocavities, pointing to a non-thermal equilibrium state inside the cavity. On the contrary, the external water vapour domain is in a thermal equilibrium state and the time scale is specified by the mean trapping time - the time a molecules travels in the outside domain before being trapped. Random walk simulations inside and outside different size nanocavities reveal the differentiation of time scales inside and outside nanocavities, pointing to an interplay between the thermodynamic state (vapor domain) and the chaotic state (nanocavity domain), leading to a variation of the number of available microstates [2]. Increment of microstates is responsible for entropy deviation during molecular water confinement, experimentally measured in complex nanocavity networks, crafted on polymeric matrixes by 157 nm vacuum ultraviolet laser light. The methodology is used for quantifying entropic variations caused by confined water or other molecules on surfaces.

[1] F. Ruggeri and M. Krishnan, “Entropic Trapping of a Singly Charged Molecule in Solution,” Nano Lett., vol. 18, no. 6, pp. 3773–3779, Jun. 2018, doi: 10.1021/acs.nanolett.8b01011.

[2] V. Gavriil, M. Chatzichristidi, D. Christofilos, G. A. Kourouklis, Z. Kollia, E. Bakalis, A.-C. C. Cefalas, and E. Sarantopoulou, “Entropy and Random Walk Trails Water Confinement and Non-Thermal Equilibrium in Photon-Induced Nanocavities,” Nanomaterials, vol. 10, no. 6, p. 1101, Jun. 2020, doi: 10.3390/nano10061101.