Search Results (12)

In this paper, we continue the study of the thermodynamics of fluid elements in isothermal turbulent self-gravitating systems, presented by molecular clouds. We build the model again on the hypothesis that, locally, the turbulent kinetic energy per fluid element can be substituted for the macro-temperature of a gas of fluid elements. Also, we presume that the cloud has a fractal nature. The virial theorem is applicable to our system too (hence it is in a dynamical equilibrium). But, in contrast to the previous work, where the turbulent kinetic energy clearly dominates over the gravity, in the present paper, we assume that the virial relation $2E_{\mathrm{kin}}+E_{\mathrm{grav}}=0$ holds for the entire cloud. Hence, the cloud is a dense and strongly self-gravitating object. On that basis, we calculate the internal and the total energy per fluid element. Writing down the first principle of thermodynamics, we obtain the explicit form of the entropy increment. It demonstrates untypical behavior. In the range $0\le \beta <0.4$, for the turbulent scaling exponent, the entropy increment is positive, but in the interval $0.4<\beta \le 1$, it is negative, and for ${\beta }_{\mathrm{cr}}=0.4$, it is zero. The latter two regimes (negative and zero) cannot be explained from the classical point of view. However, we give some arguments for the reasons for these irregularities, and the main is that our cloud is an open self-organizing system driven by the gravity. Moreover, we study the system for critical points under the conditions of three thermodynamic ensembles: micro-canonical, canonical, and grand canonical. Only the canonical ensemble exhibits a critical point, which is a maximum of the free energy and corresponds to an unstable equilibrium of the system. Analysis of the equilibrium potentials also shows that the system resides in unstable states under all the conditions. We explain these results by prompting the hypothesis that the virialized cloud is in the final unstable state before its contraction and subsequent fragmentation or collapse. Full article

Understanding the structural dynamics of semiflexible polymers in an implicit solvent under varying conditions provides valuable insights into their behavior in diverse environments. In this work, we systematically investigate the effect of the angular width of the bending potential on structural state behavior and conformational variability using microcanonical analysis. A range of angular widths is explored, with the widest value corresponding directly to the classic semiflexible polymer model, which exhibits a diverse set of structural states, including Two-Strand, Three-Strand, Four-Strand, Ring, Random Coil, and Globule configurations. As the angular width narrows, structural variability within states decreases, overlap between structural states is reduced, and conformations become more stable, leading to an expansion of the parameter space dominated by individual structures. By examining microcanonical entropy and its derivatives, we identify transitions analogous to first-, second-, and third-order thermodynamic transitions, providing a deeper understanding of the configurational landscape of semiflexible polymers. Full article

Resorting to microcanonical ensemble Monte Carlo simulations, we study the geometric and topological properties of the state space of a model of a network glass-former. This model, a Lennard-Jones binary mixture, does not crystallize due to frustration. We have found two peaks in specific heat at equilibrium and at low energy, corresponding to important changes in local ordering. These singularities were accompanied by inflection points in geometrical markers of the potential energy level sets—namely, the mean curvature, the dispersion of the principal curvatures, and the variance of the scalar curvature. Pinkall’s and Overholt’s theorems closely relate these quantities to the topological properties of the accessible state-space manifold. Thus, our analysis provides strong indications that the glass transition is associated with major changes in the topology of the energy level sets. This important result suggests that this phase transition can be understood through the topological theory of phase transitions. Full article

The vibrational dynamics of rutile (TiO₂) as a function of temperature has been studied by combining molecular dynamics (MD) simulations in conjunction with the generalized two-dimensional correlation spectroscopy analysis (2D COS) technique. Molecular dynamics simulations within the microcanonical ensemble were performed with the self-consistent charge density functional tight binding formalism at a series of different temperatures. To validate the DFTB MD results against the experimental data, the method of atomic pair distribution functions (PDFs) was used. IR absorption spectra were calculated implementing the time correlation function formalism. Subsequently, the generalized two-dimensional correlation approach was applied to obtain further insights into the temperature-dependent vibrational dynamics. The static DFTB calculations of the vibrational force field of the rutile reproduced excellently the experimental data and allowed for more exact assignments of the corresponding experimental IR/Raman spectral bands. Through the detailed analysis of the synchronous and asynchronous 2D spectra computed on the basis of MD-generated anharmonic spectra, we have provided new insights into the couplings between the modes in the studied system, as well as into the sequential character of the temperature-induced changes in the vibrational force field. The sensitivity of IR active modes to the temperature-induced perturbation of the system decreases in the order 685 cm⁻¹E_u mode > 370 cm⁻¹E_u mode > 982 cm⁻¹A_2u mode. The results presented in this study clearly demonstrate the usefulness of the combination of periodic SCC DFTB MD simulations coupled to the 2D COS analysis techniques in solid-state vibrational spectroscopy. Full article

This study investigates the density of states and structural characteristics of helical homopolymers. Comprising repeating identical units, the model enables the exploration of complex behaviors arising from a simple, yet generalized, set of potentials. Utilizing microcanonical analysis, transitions between helical structures are identified and categorized. Through a systematic comparison of results under varying conditions, we develop a nuanced understanding of the system’s general behavior. A two-dimensional plot illustrates the relative distribution of different structural types, effectively showcasing their prevalence. The findings of this study substantially advance our understanding of the density of states and structural transformations of helical homopolymers across a range of conditions. Additionally, the prevalence plot offers valuable insights into the occurrence of suppressed intermediate states, particularly in models featuring stiff helix segments. This research significantly enhances our understanding of the complex interactions governing helix bundling phenomena within the context of helical homopolymers. Full article

After reviewing several aspects about the thermodynamics of self-gravitating systems that undergo the evaporation (escape) of their constituents, some recent results obtained in the framework of fermionic King model are applied here to the analysis of galactic halos considering warm dark matter (WDM) particles. According to the present approach, the reported structural parameters of dwarf galaxies are consistent with the existence of a WDM particle with mass in the keV scale. Assuming that the dwarf galaxy Willman 1 belongs to the region III of fermionic King model (whose gravothermal collapse is a continuous phase transition), one obtains the interval 1.2 keV ≤ m ≤ 2.6 keV for the mass of WDM particle. This analysis improves previous estimates by de Vega and co-workers [Astropart. Phys. 46 (2013) 14–22] considering both the quantum degeneration and the incidence of the constituents evaporation. This same analysis evidences that most of galaxies are massive enough to undergo a violent gravothermal collapse (a discontinuous microcanonical phase transition) that leads to the formation of a degenerate core of WDM particles. It is also suggested that quantum-relativistic processes governing the cores of large galaxies (e.g., the formation of supermassive black holes) are somehow related to the gravothermal collapse of the WDM degenerate cores when the total mass of these systems are comparable to the quantum-relativistic characteristic mass $M_c={\left(\hslash c/G\right)}^{3/2}{m}^{-2}\simeq {10}^{12}{M}_{\odot }$ obtained for WDM particles with mass m in the keV scale. The fact that a WDM particle with mass in the keV scale seems to be consistent with the observed properties of dwarf and large galaxies provides a strong support to this dark matter candidate. Full article

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer’s disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes. Full article

We employ the recently introduced generalized microcanonical inflection point method for the statistical analysis of phase transitions in flexible and semiflexible polymers and study the impact of the bending stiffness upon the character and order of transitions between random-coil, globules, and pseudocrystalline conformations. The high-accuracy estimates of the microcanonical entropy and its derivatives required for this study were obtained by extensive replica-exchange Monte Carlo simulations. We observe that the transition behavior into the compact phases changes qualitatively with increasing bending stiffness. Whereas the $\Theta$ collapse transition is less affected, the first-order liquid-solid transition characteristic for flexible polymers ceases to exist once bending effects dominate over attractive monomer-monomer interactions. Full article

In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of ${\varphi }^4$ models with either nearest-neighbours and mean-field interactions. Full article

The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length $N=64$ with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the “conformational” microcanonical ( $NVU$ , where U is the potential energy) and the true microcanonical ( $NVE$ , where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature. Full article

From basic principles, we review some fundamentals of entropy calculations, some of which are implicit in the literature. We mainly deal with microcanonical ensembles to effectively compare the counting of states in continuous and discrete settings. When dealing with non-interacting elements, this effectively reduces the calculation of the microcanonical entropy to counting the number of certain partitions, or compositions of a number. This is true in the literal sense, when quantization is assumed, even in the classical limit. Thus, we build on a moderately dated, ingenuous mathematical work of Haselgrove and Temperley on counting the partitions of an arbitrarily large positive integer into a fixed (but still large) number of summands, and show that it allows us to exactly calculate the low energy/temperature entropy of a one-dimensional Bose–Einstein gas in a box. Next, aided by the asymptotic analysis of the number of compositions of an integer as the sum of three squares, we estimate the entropy of the three-dimensional problem. For each selection of the total energy, there is a very sharp optimal number of particles to realize that energy. Therefore, the entropy is ‘large’ and almost independent of the particles, when the particles exceed that number. This number scales as the energy to the power of $(2/3)$ -rds in one dimension, and $(3/5)$ -ths in three dimensions. In the one-dimensional case, the threshold approaches zero temperature in the thermodynamic limit, but it is finite for mesoscopic systems. Below that value, we studied the intermediate stage, before the number of particles becomes a strong limiting factor for entropy optimization. We apply the results of moments of partitions of Coons and Kirsten to calculate the relative fluctuations of the ground state and excited states occupation numbers. At much lower temperatures than threshold, they vanish in all dimensions. We briefly review some of the same results in the grand canonical ensemble to show to what extents they differ. Full article

The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existenceis predicted in models with extra-spatial dimensions. Full article