Entropy Density Research Articles

Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges

In the current work, we present the influence of finite volume and magnetic field on the thermodynamic properties of isospin asymmetric quark matter using the Polyakov loop extended chiral SU(3) quark mean field (PCQMF) model at finite chemical potential and temperature. Within the PCQMF model, we use the scalar and vector field values in mean-field approximation to obtain the thermodynamic properties: pressure density, entropy density and energy density. The susceptibilities of conserved charges for strongly interacting matter for different system sizes as well as for different values of the magnetic field have been studied. A sizable shift in phase boundary towards the higher values of quark chemical potential ($\mu_q$) and temperature (T) has been observed for decreasing values of system volume as well as an opposite shift towards lower temperature and quark chemical potential for increasing magnetic field. We observe an enhancement in fluctuations of conserved charges in the regime of the transition temperature. These studies may have a significant role in understanding the thermodynamic observables extracted from heavy-ion collisions data.

Hadron gas in the presence of a magnetic field using non-extensive statistics: a transition from diamagnetic to paramagnetic system

Non-central heavy-ion collisions at ultra-relativistic energies are unique in producing magnetic fields of the largest strength in the laboratory. Such fields being produced at the early stages of the collision could affect the properties of Quantum Chromodynamics matter formed in the relativistic heavy-ion collisions. The transient magnetic field leaves its reminiscence, which in principle, can affect the thermodynamic and transport properties of the final state dynamics of the system. In this work, we study the thermodynamic properties of a hadron gas in the presence of an external static magnetic field using a thermodynamically consistent non-extensive Tsallis distribution function. Various thermodynamical observables such as energy density (ϵ), entropy density (s), pressure (P) and speed of sound (c s) are studied. Investigation of magnetization (M) is also performed and this analysis reveals an interplay of diamagnetic and paramagnetic nature of the system in the presence of a magnetic field of varying strength. Further, to understand the system dynamics under equilibrium and non-equilibrium conditions, the effect of the non-extensive parameter (q) on the above observables is also studied.

An entropy-stable updated reference Lagrangian smoothed particle hydrodynamics algorithm for thermo-elasticity and thermo-visco-plasticity

This paper introduces a novel upwind Updated Reference Lagrangian Smoothed Particle Hydrodynamics (SPH) algorithm for the numerical simulation of large strain thermo-elasticity and thermo-visco-plasticity. The deformation process is described via a system of first-order hyperbolic conservation laws expressed in referential description, chosen to be an intermediate configuration of the deformation. The linear momentum, the three incremental geometric strains measures (between referential and spatial domains), and the entropy density of the system are treated as conservation variables of this mixed coupled approach, thus extending the previous work of the authors in the context of isothermal elasticity and elasto-plasticity. To guarantee stability from the SPH discretisation standpoint, appropriate entropy-stable upwinding stabilisation is suitably designed and presented. This is demonstrated via the use of the Ballistic free energy of the coupled system (also known as Lyapunov function), to ensure the satisfaction of numerical entropy production. An extensive set of numerical examples is examined in order to assess the applicability and performance of the algorithm. It is shown that the overall algorithm eliminates the appearance of spurious modes (such as hour-glassing and non-physical pressure fluctuations) in the solution, typical limitations observed in the classical Updated Lagrangian SPH framework.

Features of hadronic and deconfined matter in a range of collision energies spanning from the BNL Alternating Gradient Synchrotron to the CERN Large Hadron Collider

Previous extensive studies on the dependence of the average transverse momentum, its slope as a function of the hadron mass, and the average transverse expansion on the particle multiplicity per unit rapidity and unit transverse overlap area of the colliding partners are extended to the ratio of the energy density to the entropy density. The behavior of the ratio between the average transverse momentum and the square root of the particle multiplicity per unit rapidity and unit transverse overlap area $\ensuremath{\langle}{p}_{T}\ensuremath{\rangle}/\sqrt{\ensuremath{\langle}dN/dy\ensuremath{\rangle}/{S}_{\ensuremath{\perp}}}$ as a function of collision energy for a given centrality or as a function of centrality for a given collision energy supports the predictions of color glass condensate and percolation based approaches. The dependence of the ratio of the energy density $\ensuremath{\langle}d{E}_{T}/dy\ensuremath{\rangle}/{S}_{\ensuremath{\perp}}$ to the entropy density $\ensuremath{\langle}dN/dy\ensuremath{\rangle}/{S}_{\ensuremath{\perp}}$ at different collision centralities for $A\text{\ensuremath{-}}A$ collisions from the Alternating Gradient Synchrotron, the Super Proton Synchrotron, the BNL Relativistic Heavy Ion Collider, and the CERN Large Hadron Collider energies is presented. The trend of this ratio towards a plateau at the highest RHIC energies followed by a steep rise at LHC energies is in agreement with theoretical predictions made 40 years ago that indicate this behavior as a signature of a phase transition. This pattern strongly depends on the collision geometry, converging towards the dependence that characterizes the $pp$ minimum bias collisions for the most peripheral $A\text{\ensuremath{-}}A$ collisions. Expected similarities between $pp$ and Pb-Pb collisions at LHC energies are confirmed.

Islands in the fluid: islands are common in cosmology

We discuss the possibility of entanglement islands in cosmological spacetimes with a general perfect fluid with an equation of state w. We find that flat universes with time-symmetric slices where the Hubble parameter vanishes always have islands on that slice. We then move away from such slices, considering still universes with a general perfect fluid. Under the local thermal equilibrium assumption, the comoving entropy density sc is constant. As a result, the conditions for an island become an inequality between the energy density (or Hubble parameter) and the temperature at some time of normalization. The consequences are that islands can exist for practically all fluids that are not radiation, i.e. w ≠ 1/3. We also discuss the ramifications of our results for universes with spatial curvature. Finally, we show that islands occur in the Simple Harmonic Universe model which has no classical singularity at the background level, in contrast to all previous examples where islands occurred only in space-times with singularities.

Equations-of-state deduced form different types of black holes

Black holes are seen as thermodynamical systems. They can be characterized by thermodynamic intensive quantities such as temperature, pressure, and extensive quantities such as entropy and energy density. In this paper, we focus on the thermodynamical properties of (a) Schwarzschild, (b) Reissner–Nordström, (c) Kerr, and (d) Kerr–Newman black holes. These allow to estimate the corresponding equations-of-state (EoS) and the squared speed of sound for each of them. The latter helps to calculate the ratio of the bulk viscosity to the shear viscosity for each of the black holes. We conclude that the resulting EoS enhances when moving from Schwarzschild to Reissner–Nordström to Kerr, and to Kerr–Newman black holes.

Gravastar in the framework of symmetric teleparallel gravity* *SP & PKS acknowledges the National Board for Higher Mathematics (NBHM) under the Department of Atomic Energy (DAE) of the government of India for financial support to carry out the research project (02011/3/2022 NBHM(R.P.)/R & D II/2152 Dt.14.02.2022)

We present a novel gravastar model based on the Mazur-Mottola (2004) method with an isotropic matter distribution in gravity. The gravastar, which is a hypothesized substitute for a black hole, is built using the Mazur-Mottola mechanism. This approach allows us to define the gravastar as having three stages. The first one is an inner region with negative pressure; the next region is a thin shell that is made up of ultrarelativistic stiff fluid, and we studied the proper length, energy, entropy, and surface energy density for this region. Additionally, we demonstrated the possible stability of our suggested thin shell gravastar model through the graphical study of the surface redshift. The exterior Schwarzschild geometry describes the outer region of the gravastar. In the context of gravity, we discovered analytical solutions for the interior of gravastars that are free of any type of singularity and the event horizon.

Relativistic transformation of thermodynamic parameters and refined Saha equation

The relativistic transformation rule for temperature is a debated topic for more than 110 years. Several incompatible proposals exist in the literature but a final resolution is still missing. In this work, we reconsider the problem of relativistic transformation rules for a number of thermodynamic parameters including temperature, chemical potential, pressure, entropy and enthalpy densities for a relativistic perfect fluid using relativistic kinetic theory. The analysis is carried out in a fully relativistic covariant manner, and the explicit transformation rules for the above quantities are obtained in both Minkowski and Rindler spacetimes. Our results suggest that the temperature of a moving fluid appears to be colder, supporting the proposal by de Broglie, Einstein, and Planck, in contrast to other proposals. Moreover, in the case of a Rindler fluid, our findings suggest that the total number of particles and the total entropy of a perfect fluid in a box whose bottom is parallel to the Rindler horizon are proportional to the area of the bottom, but are independent of the height of the box, provided the bottom of the box is sufficiently close to the Rindler horizon. The area dependence of the particle number implies that the particles tend to be gathered toward the bottom of the box, and hence implicitly determines the distribution of the chemical potential of the system, whereas the area dependence of the entropy indicates that the entropy is still additive and may have potential applications in explaining the area law of black hole entropy. As a by-product, we also obtain a relativistically refined version of the famous Saha equation which holds in both Minkowski and Rindler spacetimes.

A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics

In this paper we propose a novel thermodynamically compatible finite volume scheme for the numerical solution of the equations of magnetohydrodynamics (MHD) in one and two space dimensions. As shown by Godunov in 1972, the MHD system can be written as overdetermined symmetric hyperbolic and thermodynamically compatible (SHTC) system. More precisely, the MHD equations are symmetric hyperbolic in the sense of Friedrichs and satisfy the first and second principles of thermodynamics. In a more recent work on SHTC systems, \cite{Rom1998}, the entropy density is a primary evolution variable, and total energy conservation can be shown to be a \textit{consequence} that is obtained after a judicious linear combination of all other evolution equations. The objective of this paper is to mimic the SHTC framework also on the discrete level by directly discretizing the \textit{entropy inequality}, instead of the total energy conservation law, while total energy conservation is obtained via an appropriate linear combination as a \textit{consequence} of the thermodynamically compatible discretization of all other evolution equations. As such, the proposed finite volume scheme satisfies a discrete cell entropy inequality \textit{by construction} and can be proven to be nonlinearly stable in the energy norm due to the discrete energy conservation. In multiple space dimensions the divergence-free condition of the magnetic field is taken into account via a new thermodynamically compatible generalized Lagrangian multiplier (GLM) divergence cleaning approach. The fundamental properties of the scheme proposed in this paper are mathematically rigorously proven. The new method is applied to some standard MHD benchmark problems in one and two space dimensions, obtaining good results in all cases.

Induction of epithelial to mesenchymal transition in HPV16 E6/E7 oncogene transfected C33A cell line

This study focuses on the induction of EMT by HPV16 in the C33A cell line. Expression of β-catenin, EMT-transcription factors (EMT-TFs), and c-myc in the nuclei of HPV16 E6/E7 oncogene transfected and non-transfected C33A cells were investigated through immunofluorescence and RT-PCR. Microphotographs of β-catenin, c-myc, and DAPI-stained nuclei were processed and analyzed by Python and ImageJ respectively. Microphotographs of immunocytochemically stained transfected and control cells were then processed and analyzed with the help of ImageJ and Python programming. The intensity and the integrated density of β-catenin were computed at the cell membrane area as well as the cytoplasmic area along with the integrated density of c-myc and Renyi entropy of DAPI-stained nuclei was quantified by ImageJ software. Python programming was implemented to determine the total percentage of white pixels depicting the presence of β-catenin in the cytoplasmic area of cells. The signal of β-catenin at the cytoplasmic area was found significantly higher in transfected samples which implies the nuclear accumulation of β-catenin. The expression of the c-myc protein was found significantly higher in transfected cells along with significantly higher nuclear entropy. RT-PCR result shows two folds of up-regulation of EMT-TFs Snail1, Twist1, and Zeb2 and down-regulation of Snail2 and Twist2. The study concludes that HPV16 E6/E7 oncogene can induce EMT.

Thermodynamic properties of non-Hermitian Nambu–Jona-Lasinio models

We investigate the impact of non-Hermiticity on the thermodynamic properties of interacting fermions by examining bilinear extensions to the $3+1$ dimensional $SU(2)$-symmetric Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics at finite temperature and chemical potential. The system is modified through the anti-$PT$-symmetric pseudoscalar bilinear $\bar{\psi}\gamma_5 \psi$ and the $PT$-symmetric pseudovector bilinear $iB_\nu \,\bar{\psi}\gamma_5\gamma^\nu \psi$, introduced with a coupling $g$. Beyond the possibility of dynamical fermion mass generation at finite temperature and chemical potential, our findings establish model-dependent changes in the position of the chiral phase transition and the critical end-point. These are tunable with respect to $g$ in the former case, and both $g$ and $|B|/B_0$ in the latter case, for both lightlike and spacelike fields. Moreover, the behavior of the quark number, entropy, pressure, and energy densities signal a potential fermion or antifermion excess compared to the standard NJL model, due to the pseudoscalar and pseudovector extension respectively. In both cases regions with negative interaction measure $I = \epsilon-3p$ are found. Future indications of such behaviors in strongly interacting fermion systems, for example in the context of neutron star physics, may point toward the presence of non-Hermitian contributions. These trends provide a first indication of curious potential mechanisms for producing non-Hermitian baryon asymmetry. In addition, the formalism described in this study is expected to apply more generally to other Hamiltonians with four-fermion interactions and thus the effects of the non-Hermitian bilinears are likely to be generic.

Thermo-mechanical aging during churning in grease lubricated bearings and its impact on grease life

Grease aging in a rolling bearing happens primarily during the churning phase due to high shear and temperature caused by macroscopic flow. This study utilizes a temperature profile to quantify the impact of thermo-mechanical aging on grease. Two different methods are explored to evaluate the energy dissipated in the grease during churning: one estimates the imposed energy density and the other calculates the heat transfer entropy density. Both models show a good correlation with the measured grease life. Grease life test results show that a high imposed energy density or heat transfer entropy density during churning results in shorter grease life. Therefore, a low energy density or heat transfer entropy density is preferred during churning.

Complementary two-particle correlation observables for relativistic nuclear collisions

Two-particle correlations are a widely used tool for studying relativistic nuclear collisions. Multiplicity fluctuations comparing charge and particle species have been studied as a possible signal for quark-gluon plasma (QGP) and the QCD critical point. These fluctuation studies all make use of particle variances which can be shown to originate with a two-particle correlation function. Momentum correlations and covariances of momentum fluctuations, which arise from the same correlation function, have also been used to extract properties of the nuclear collision medium such as the shear viscosity to entropy density ratio, the shear relaxation time, and temperature fluctuations. Searches for critical fluctuations are also done with these correlation observables. We derive a mathematical relationship between several number and momentum density correlation observables and outline the different physics mechanisms often ascribed to each. This set of observables also contains a new multiplicity-momentum correlation. Our mathematical relation can be used as a validation tool for measurements, as a method for interpreting the relative contributions of different physics mechanisms on correlation observables, and as a test for theoretical and phenomenological models to simultaneously explain all observables. We compare an independent source model to simulated events from pythia for all observables in the set.

Driven one-dimensional noisy Kitaev chain

We study a one-dimensional Kitaev chain driven by the anisotropy parameter ${J}_{\ensuremath{-}}=t/{\ensuremath{\tau}}_{Q}$, in the presence of weak Gaussian noise in the parameter ${J}_{+}$. The system is prepared in the ground state of the Hamiltonian at the initial time $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. The defect density and the residual energy at the end of the drive protocol reveals anti-Kibble Zurek (AKZ) behavior which deviates from the earlier reported linear in quench time dependence for the defect density. The entropy density at the end of the protocol is found to exhibit the signature of the AKZ behavior. In the context of the Kitaev chain, the two-point spin correlators are short ranged. The hidden topological order across the quantum phase transition point is probed via the nonlocal string order parameters. The two-point Majorana correlator and the hidden string correlator calculated in the final decohered state at the end of the noisy drive protocol is consistent with the AKZ picture. We have analyzed the kink statistics in the dual spin space, the first three cumulants at the end of the noisy drive also exhibit the AKZ scaling behavior for slower sweeps similar to the defect density. The kink distribution function is well approximated with the normal distribution with nonuniversal noise dependent mean and variance.

Constitutive and numerical modeling for the coupled thermal-hydro-mechanical processes in dual-porosity geothermal reservoir

Enhanced geothermal system (EGS) is viewed as one of the most practical methods to explore geothermal energy in hot dry rock (HDR), which can contribute to zero carbon emissions and provide reliable and renewable energy. Modelling the performance and long-term environmental effects of the EGS remains a challenge as the rock is often fractured and experiences complicated multi-physics coupling behaviour. Despite studies on constitutive or numerical modelling of coupled behaviour in deformable dual-porosity media, those developed models often ignore the fully coupled processes in heat transfer and are highly empirical. Based on a non-equilibrium thermodynamics approach, the Mixture-Coupling Theory, this research derives the fully coupled Thermo-Hydro-Mechanical (THM) governing equations for dual-porosity geothermal reservoirs, addressing the interaction between strain, pore/fracture pressure and temperature. The constitutive model is obtained by the analysis of Helmholtz free energy evolution in dual-porosity reservoirs. The proposed model determines the fully coupled evolution of solid stress, both pore and fracture porosity, and solid entropy density. The governing equations can predict the fully coupled THM effect in dual-porosity geothermal reservoirs. Numerical modelling is then performed to study the production performance and coupled THM response in an EGS. The modelling results show that the production temperature is determined by the coupled THM effects. Porosity change is mainly determined by temperature change (accounting for over 87% of the total porosity change) during the extraction. The porosity change accounts for 1.03% and 1.23% of the initial porosity for pore and fracture, separately.

К выводу в рамках статистики Тсаллиса релятивистского кинетического уравнения для разреженной идеальной газовой системы высокоэнергетических частиц

In this work we discuss the nonextensive kinetic theory for anomalous gas q-systems in a general relativistic framework. By including nonextensive effects in the collision term of the relativistic equation (violating Boltzmann molecular chaos hypothesis) and in a modified 4-vector expression for the q-entropy flux it is shown that the entropic Tsallis formalism preserves a local form of the relativistic H-theorem according to which the entropy growth in any point of space-time is never negative. It is shown that the local collision equilibrium (the zero-point entropy source term) is described by a generalized version of the Yuttner relativistic distribution. Using this distribution, the particle number, energy and entropy densities and the thermal equation of state for a relativistic q-gas of identical particles in the equilibrium state are determined explicitly. The results are reduced to the standard ones in the extensive limit, thus showing that the nonex-tensive entropic scheme can be consistent with the space-time ideas contained in the general rela-tivistic theory. The constructed kinetic equation is designed to describe a wide range of phenomena in as-trophysics, cosmology and high-energy physics, in particular, multiparticle production processes in relativistic collisions.

Interaction of <sup>28</sup>Si with Emulsion Nuclei at 4.5 AGeV/c in View of Thermo-Statistical Approach

In this work, we study some changes of nuclear matter in the interactions of 28S with emulsion nuclei at 4.5 AGeV/c. From the experimental quantities investigated using Tsallis’ statistics, we deduced the temperature, entropy density and non-equilibrium factor of the nuclear medium. These obtained parameters were used to reveal variations in the nuclear matter at the stated interaction energy. The results that came up from this study were compared with their corresponding results obtained from other heavy ion collision experiments at wide energy range.

The EEG Oscillations and Psychology Propensities of Autonomous Sensory Meridian Response.

Autonomous sensory meridian response is believed as a perceptual phenomenon to specific sensory stimuli. To explore the underlying mechanism and emotional effect, the EEG under video and audio triggers of autonomous sensory meridian response was analyzed. The differential entropy and power spectral density by Burg method on δ, θ, α, β, γ and high γ frequencies were employed as quantitative features. The results indicate that the modulation of autonomous sensory meridian response on brain activities is broadband. Video trigger owns better performance of autonomous sensory meridian response than other triggers. Moreover, the results also reveal that autonomous sensory meridian response has a close relationship with neuroticism and its three sub-dimensions, anxiety, self-consciousness and vulnerability, with the scores of self-rating depression scale, but without emotions, happiness, sadness, or fear. This suggests that the responders of autonomous sensory meridian response may have the tendencies of neuroticism and depressive disorder.

Immune repertoire and responses to neoadjuvant TCHP therapy in HER2-positive breast cancer.

Despite the introduction of trastuzumab, pathologic complete response (pCR) is not attained in approximately 30-40% of Human epithelial growth factor receptor-2-positive breast cancer. Tumor-infiltrating lymphocytes (TIL) have been suggested as a predictive marker of treatment response, albeit not always effective. We investigated the relationship between trastuzumab, docetaxel, carboplatin, and pertuzumab (TCHP) treatment and immune repertoire as a treatment response predictor. In all, 35 cases were divided into two experimental groups: 10 and 25 cases in the preliminary and main experiments, respectively. In the preliminary experiment, the biopsy tissues before TCHP treatment and the surgical tissues after TCHP treatment were compared. In the main experiment, the biopsy tissues before TCHP treatment were compared according to the TCHP treatment response. The T-cell repertoire for TRA, TRB, TRG, and TRD, and B-cell repertoire for immunoglobulin heavy, immunoglobulin kappa, and immunoglobulin lambda were evaluated. Whole transcriptome sequencing was also performed. In the preliminary experiment, the density and richness of the T-cell receptor (TCR) and B-cell receptor (BCR) repertoires decreased after treatment, regardless of TCHP response. In the main experiment, the Shannon's entropy index, density, and length of CDR3 of the TCR and BCR repertoires did not differ significantly in patients who did and did not achieve pCR. The pCR and non-pCR subgroups according to the level of TILs revealed that the non-pCR/lowTIL group had a higher proportion of low-frequency clones than the pCR/lowTIL group in TRA (non-pCR/lowTIL versus pCR/lowTIL, 0.01-0.1%, 63% versus 45.3%; <0.01%, 32.9% versus 51.8%, p < 0.001) and TRB (non-pCR/lowTIL versus pCR/lowTIL, 0.01-0.1%, 26.5% versus 14.7%; <0.01%, 72.0% versus 84.1%, p < 0.001). The role of the diversity, richness, and density of the TCR and BCR repertoires as predictive markers for TCHP response was not identified. Compositions of low-frequency clones could be candidates for predictive factors of TCHP response; however, validation studies and further research are necessary.

Emergence of biological transportation networks as a self-regulated process

We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal $L^2$-gradient flow for the symmetric tensor valued diffusivity $D$ of a broad class of entropy dissipations associated with a purely diffusive model. The introduction of a prescribed electric potential leads to the Fokker-Planck equation, for whose entropy dissipations we also investigate the formal $L^2$-gradient flow. We derive an integral formula for the second variation of the dissipation functional, proving convexity (in dependence of diffusivity tensor) for a quadratic entropy density modeling Joule heating. Finally, we couple in the Poisson equation for the electric potential obtaining the Poisson-Nernst-Planck system. The formal gradient flow of the associated entropy loss functional is derived, giving an evolution equation for $D$ coupled with two auxiliary elliptic PDEs.