Free Internal Energy Research Articles

A thermophysical mechanism exploration of the brain: Motor cortex modeling with canonical ensemble theory

The brain, recognized as one of the most intricate systems globally, has been a focal point for scientific exploration. Researchers have made efforts to construct models of the brain based on neural dynamics and complex networks to gain insights into its workings. It is crucial to investigate the brain's working principles from various perspectives. This study presents a novel thermophysical model of the motor cortex and examines its potential thermodynamic properties. Utilizing canonical ensemble theory, we constructed the thermophysical model using spike and local field potential (LFP) signals obtained from intracortical brain-machine-interfaces (iBMIs) in two monkeys. The parameters derived from this model—namely internal energy, free energy, and entropy—were employed to assess the thermodynamic properties and observe alterations in these properties during reaching and grasping movements. Furthermore, this proposed model was applied to movement pattern decoding, highlighting its potential in neural decoding tasks. In both LFP- and spike-based thermodynamic models, there was an increase in internal energy and free energy, coupled with a decrease in entropy when the motor cortex was activated across various movement tasks. This suggests that the neural system adheres to the principles of a thermophysical system. Notably, the thermodynamic features demonstrated superior performance in decoding movement intentions compared to traditional LFP and spike features. This study represents the first construction of a comprehensive thermodynamic model of the motor cortex based on LFP and spike signals. The model exhibits remarkable stationarity and holds promise for long-term and stable evaluations of motor cortex functions.

Investigation on the structural, elastic, electronic, thermodynamic, and vibrational properties of the full heusler Sc2XAl (X =Cd and Zn): An ab initio study

The structural, mechanical, electronic, thermodynamic, and phonon characteristics of Sc2CdAl and Sc2ZnAl in L21 phase were the main focuses on this investigation. The density of states (DOS) and electronic band spectra signify the metallic behavior of the L21 phase of both materials. The impact of atomic arrangement with respect to the Wyckoff sites on the mechanical stability were additionally studied. The elastic constants of Sc2CdAl and Sc2ZnAl alloys indicated that these alloys convened Born mechanical stability criteria. Using the density functional perturbation theory's first-principle linear response method, complete phonon spectra have been acquired. Moreover, the quasi-harmonic approximation, specific heat capacity at constant volume, the internal free energy, entropy, and vibrational free energy variations of Sc2CdAl and Sc2ZnAl as full Heusler alloys have been utilized in examination the change over the temperature between 0 and 800 K. Both alloys might find application in real industrial applications.

[formula omitted]-dimensional Klein–Gordon equation in presence of deformed generalized Deng–Fan with Yukawa potential class: Approximate bound state solutions in relativistic and non-relativistic regimes

In this paper, we examine the bound state solutions of the D-dimensional Klein–Gordon equation for a deformed Deng–Fan potential in generalized form along with Yukawa potential class. The supersymmetric quantum mechanics method and Nikiforov–Uvarov method are employed, utilizing a proper correspondence to the centrifugal potential term. Remarkably, in both methods, we obtain the same analytical expressions for normalized wave functions and energy eigenvalues, expressed in closed form by hypergeometric functions and Jacobi polynomials, for all l and n quantum states. Additionally, we explore the thermodynamic quantities (internal energy, partition function, specific heat, entropy and free energy) in case of both relativistic and non-relativistic regimes for the aforementioned potential. Finally, we demonstrate energy variation against various potential parameters for a few diatomic molecules pictorially.

A New Non-Extensive Equation of State for the Fluid Phases of Argon, Including the Metastable States, from the Melting Line to 2300 K and 50 GPa

A new equation of state for argon was developed with the view of extending the range of validity of the equation of state previously proposed by Tegeler et al. and obtaining a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase, metastable, and saturation states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However, in this work, the fundamental equation for Helmholtz free energy was derived from the measured quantities CV(ρ, T) and P(ρ, T). The empirical description of the isochoric heat capacity CV(ρ, T) was based on an original empirical description explicitly containing the metastable states. The thermodynamic properties (internal energy, entropy, and free energy) were then obtained by combining the integration of CV(ρ, T). The arbitrary functions introduced by the integration process were deduced from a comparison between calculated and experimental pressure P(ρ, T) data. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 GPa. It also predicts the existence of a maximum of the isochoric heat capacity CV along isochors, as experimentally observed in several other fluids. For many applications, an approximate form of the equation of state for the liquid phase may be sufficient. A Tait–Tammann equation is therefore proposed between the triple-point temperature and 148 K.

Using small database and energy descriptors to predict molecular thermodynamic energies through mediated learning models

Delta machine learning (DML) models have paved a new way to obtaining high fidelity ab initio simulation results of materials by using quantities with lower computational cost as learning materials. However, the low out-of-sample extrapolative ability and the requirement of large training sets have limited broader applications of conventional DML models. In this work, we proposed the concept of non-trivial electron energy, an intermediary energy quantity decoded from the electron total energy but exhibiting high Pearson's correlation with various thermodynamic energies, to build up mediated machine learning (MML) models. By hybridizing the intermediary non-trivial electron energy (N) with a bond descriptor (B) and a spatial matrix (S) of organic molecules, our integrated NBS descriptor shows excellent predictive power of thermodynamic energies with errors close to 1 kcal/mol for MML models when trained by a database with 100 entries and tested by a database with 500 entries. Moreover, adding supplemental sets with 10 ∼ 20 entries into the original training set could greatly improve the out-of-sample extendibility of NBS MML models, such as the molecules with obviously larger size, with disparate bond-type, and even with different elemental compositions. The method of mediated learning provides alternative ways to breakthrough limitations of traditional DML models and can be applied conveniently to study formation enthalpy, thermodynamic energy barriers, multi-dimensional Gibbs free energy surface, and other quantum chemical quantities related to materials' internal energy, enthalpy, and free energy under various conditions at tunable training cost, prediction efficiency, and accuracy.

Dynamical free energy based model for quantum decision making

We propose a quantum-mechanical framework to describe the dynamics of human decision making, where the interactions between the open quantum system of decision makers and its surrounding environment at given temperature are relevantly taken into account. The temporal evolution of quantum system is described in terms of the time-dependent density matrix, from which we can evaluate those thermodynamic functions such as internal energy, (von Neumann) entropy and (Helmholtz) free energy. In this study we rely on the symmetrical quasi-classical (SQC) windowing approach to numerically solve the non-adiabatic quantum dynamics. We then consider the Hamiltonians to formulate the Prisoner’s Dilemma (PD) problem and calculate the population dynamics of the quantum states of two players’ decisions, where some quantum coherence or interference effects are observed. The evaluated free energy tends to decrease toward the thermodynamic equilibrium value, thus driving the dynamics of quantum system between the Nash equilibrium and Pareto optimum states. The calculated entropy often shows a tendency of temporal decrease, thus indicating the emergence of order in the quantum system. We have also applied the present scheme to the issue of the violation of the sure thing principle and found its occurrence through explicit numerical simulations for the PD problem. The present study may provide a theoretical basis to connect the dynamics of quantum decision making to the free energy principle in cognitive science.

Thermal Casimir effect in a classical liquid in a quasiperiodically identified conical spacetime

In this paper, we study the finite-temperature quantum fluctuation of a classical liquid induced by the topology of an effective conical spacetime, as well as by a quasiperiodic boundary condition. The conical spacetime could be either a disclination or a cosmic string. In this context, we consider a phonon field representing quantum excitations of the liquid density, which obeys an effective Klein-Gordon equation with the sound velocity replaced by the light velocity. We obtain closed analytic expressions for the thermal Hadamard function, and consequently, the renormalized mean square density fluctuation of the liquid along with thermodynamics quantities such as internal energy, free energy, total energy, and entropy densities. We also discuss the limiting cases, including low- and high-temperature regimes, and the situations in which there is only either the conical spacetime or quasiperiodicity.

Fundamentals and mechanics of polyelectrolyte gels: Thermodynamics, swelling, scattering, and elasticity

Polyelectrolyte gels are ionizable, crosslinked polymer networks swollen in a solvent. These materials are prevalent in biological and synthetic applications ranging from the extracellular matrix to personal care products because they swell and deswell according to changes in the solution environment and internal structure. These environmental and internal factors include temperature, solvent, salt, pH, polymer volume fraction, and crosslink density. In order to predict useful properties like swelling and modulus, 70+ years of effort have been taken to understand the thermodynamic driving forces that affect polyelectrolyte gels. Here, we consider the current thermodynamic model of polyelectrolyte gel behavior, which includes balancing the mixing, electrostatic, Donnan, and elastic osmotic pressures, and we present current experimental results in the context of this model. Since the internal free energy of polyelectrolyte gels results in structural and modulus changes, we also review how thermodynamics are linked to rheological and scattering studies. Due to the complex nature of polyelectrolyte gels, the influence of the solution environment on gel behavior and structure has been investigated; however, the current findings are convoluted with multiple equilibrium states and there is a need for greater understanding of the influence of counterion condensation, interfaces, and inhomogeneities. By describing the current state of the thermodynamic model for polyelectrolyte behavior, we emphasize the complexity and tunability of polyelectrolyte gels for future applications. We propose the future direction of polyelectrolyte gel research to focus on gels at interfaces, in human biology, and on gel inhomogeneities. However, these future directions require an understanding of polyelectrolyte gel mechanical properties, structure, and complex nature that can be understood using the current thermodynamic model.

Folding Free Energy Surfaces from Differential Scanning Calorimetry.

Protein folding/unfolding processes involve a large number of weak, non-covalent interactions and are more appropriately described in terms of the movement of a point representing protein conformation in a plot of internal free energy versus conformational degrees of freedom. While these energy landscapes have an astronomically large number of dimensions, it has been shown that many relevant aspects of protein folding can be understood in terms of their projections onto a few relevant coordinates. Remarkably, such low-dimensional free energy surfaces can be obtained from experimental DSC data using suitable analytical models. Here, we describe the experimental procedures to be used to obtain the high-quality DSC data that are required for free-energy surface analysis.

Strain gradient elasto-plasticity model: 3D isogeometric implementation and applications to cellular structures

In the present work, we combine Mindlin’s strain gradient elasticity theory and Gudmundson–Gurtin–Anand strain gradient plasticity theory to form a unified framework. The gradient plasticity model is enriched by including the gradient of elastic strains into the expression of the internal virtual work and free energy. This augments the modelling capabilities by incorporating elasticity-related length scales along with plasticity-related energetic and dissipative ones. The strong form governing equations are derived via the principle of virtual work addressing a complete set of boundary conditions. The fourth-order boundary value problem of the gradient elasto-plasticity model is then formulated in a variational form within an H2 Sobolev space setting. Conforming Galerkin discretizations for numerical results are obtained utilizing an isogeometric approach with NURBS basis functions of degree p≥2 providing Cp−1-continuity. The implementation follows a viscoplastic constitutive framework and adopts the backward Euler time integration scheme. A set of benchmark examples is considered to illustrate convergence properties and to accomplish parameter studies. It is shown that the elastic length scale parameter controls the slope of the elastic part and causes an additional hardening in the plastic part of the material response curves. Finally, an illustrative example is considered in order to demonstrate the applicability of both the continuum model and the numerical method in capturing the size-dependent torsion response of cellular structures.

Temperature and Composition Dependent Structural Evolution: Thermodynamics of CunAg135-n (n = 0-135) Nanoalloys during Cooling.

Molecular dynamics simulations are performed to investigate the changes of packing structures, and thermodynamic quantities including internal energy, entropy, and free energy are used to determine temperature regime and transition time of atomic packing structures. The simulation results show different packing structures as the component composition changes, and there are different packing patterns during cooling. For these Cu-Ag alloy clusters containing only a small number of atoms of Cu, they present FCC packing structures in different parts at high temperatures, and then there are transformations to icosahedral structures. With the increase in content of Cu atoms, there is a transition mechanism from molten state to icosahedron. When the content of Cu atoms is appropriate, core-shell structures can be formed at room temperature.

Thermodynamics of phase equilibrium in solid-liquid and solid-gas systems

The thermodynamic equilibrium of a two-phase system is described by the Gibbs equation, which includes state parameters. On the basis of the Gibbs equation and the combined equation of the first and second laws of thermodynamics, thermodynamic potentials are written: internal energy, enthalpy and Gibbs free energy. If the two phases are in equilibrium, then the temperatures, pressures and chemical potentials of these phases are equal to each other. Equalities express the conditions of thermal and mechanical equilibrium, as well as the condition for the absence of a driving force for the transfer of a component across the interface. For a two-phase system, the Gibbs-Duhem equation connects the volume and entropy of 1 mole of the mixture, the content of any component, expressed in mole fractions. Extraction from lupine particles with cheese whey (solid-liquid system) is considered. The driving force of the extraction process in the solid-liquid system is the difference between the concentration of the solvent at the surface of the solid C and its average concentration C0 in the bulk of the solution. The concentration at the interface is usually taken to be equal to the concentration of a saturated solution of Cn, since equilibrium is established rather quickly near the surface of a solid. Then the driving force of the process is expressed as Cn – C0. A curve for the extraction of extractives from lupine with cheese whey was plotted by superimposing low-frequency mechanical vibrations.

Linear isotherm regularities of solid sodium under pressure

We propose several new regularities in solid sodium from the available experimental data and calculated thermodynamic properties along the isotherms with the equation of state (EOS) of the modified Holzapfel form. Z−1V2 is a linear function in terms of V2 with different intersection points for the isotherms at high temperatures within the considered pressure range, where Z and V are the compressibility factor and molar volume. The calculated isothermal bulk modulus BT and internal pressure Pint of solid sodium vary almost linearly with pressure. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT from the modified Holzapfel EOS are observed to be linear with respect to V−2 with temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity EOS. In addition, analytical expressions of the thermodynamic properties of solid sodium are derived from the linear isothermal regularity EOS, such as internal energy, entropy, enthalpy, free energy, and heat capacity.

First-principles calculations to investigate the structural, electronic, elastic, vibrational and thermodynamic properties of the full-Heusler alloys X2ScGa (X = Ir and Rh)

This study has investigated ab initio pseudopotential calculations on the structural, electronic, elastic, vibrational and thermodynamic properties of the full-Heusler X2ScGa (X = Ir and Rh) alloys. The calculations have taken place under consideration of the generalized gradient approximation (GGA) of the density functional theory (DFT) with using the plane-wave ab initio pseudopotential method. According to the calculations, the major contribution to electronic states at the Fermi energy has been achieved by d orbitals, revealing a more active role for transition metals Ir (Rh) and Sc atoms. The reckonings point out that the Ir2ScGa and Rh2ScGa have metallic behavior at the equilibrium lattice constant with the density of states (DOS) at the Fermi level (N (EF)) of 1.412 states/eV and 1.821 states/eV, respectively. The results of the elastic constants showed that these compounds met the criteria for Born mechanical stability. It was also observed that they have a ductile structure and exhibit anisotropic behavior according to Pugh criteria. Besides, the full phonon spectra and their projected partial density of states of the alloys have been analyzed with the first-principle linear-response approach of the density-functional perturbation theory. All the alloys behaved dynamically stable in the L21 phase. Furthermore, internal free energy, entropy, specific heat capacity at constant volume and vibrational free energy changes of Ir2ScGa and Rh2ScGa alloys were analyzed and discussed between the temperature range of 0–800 K using the quasi harmonic approximation. According to the results, these alloys are potential candidate for industrial use.

A thermodynamic transient cross-bridge model for prediction of contractility and remodelling of the ventricle

Cardiac hypertrophy is an adaption of the heart to a change in cardiovascular loading conditions. The current understanding is that progression may be stress or strain driven, but the multi-scale nature of the cellular remodelling processes have yet to be uncovered. In this study, we develop a model of the contractile left ventricle, with the active cell tension described by a thermodynamically motivated cross-bridge cycling model. Simulation of the transient recruitment of myosin results in correct patterns of ventricular pressure predicted over a cardiac cycle. We investigate how changes in tissue loading and associated deviations in transient force generation can drive restructuring of cellular myofibrils in the heart wall. Our thermodynamic framework predicts in-series sarcomere addition (eccentric remodelling) in response to volume overload, and sarcomere addition in parallel (concentric remodelling) in response to valve and signalling disfunction. This framework provides a significant advance in the current understanding of the fundamental sub-sarcomere level biomechanisms underlying cardiac remodelling. Simulations reveal that pathological tissue loading conditions can significantly alter actin-myosin cross-bridge cycling over the course of the cardiac cycle. The resultant variation in sarcomere stress pushes an imbalance between the internal free energy of the myofibril and that of unbound contractile proteins, initiating remodelling. The link between cross-bridge thermodynamics and myofibril remodelling proposed in this study may significantly advance current understanding of cardiac disease onset.

New Zirconium Diboride Polymorphs-First-Principles Calculations.

Two new hypothetical zirconium diboride (ZrB) polymorphs: (hP6-P6/mmc-space group, no. 194) and (oP6-Pmmn-space group, no. 59), were thoroughly studied under the first-principles density functional theory calculations from the structural, mechanical and thermodynamic properties point of view. The proposed phases are thermodynamically stable (negative formation enthalpy). Studies of mechanical properties indicate that new polymorphs are less hard than the known phase (hP3-P6/mmm-space group, no. 191) and are not brittle. Analysis of phonon band structure and density of states (DOS) also show that the phonon modes have positive frequencies everywhere and the new ZrB phases are not only mechanically but also dynamically stable. The estimated acoustic Debye temperature, , for the two new proposed ZrB phases is about 760 K. The thermodynamic properties such as internal energy, free energy, entropy and constant-volume specific heat are also presented.

A novel critical behavior of the spin-1 Blume–Capel model with a distance-dependent nearest-neighbor exchange interaction and magneto-elastic coupling

A generalized spin-1 Blume–Capel model with distance/volume dependent nearest-neighbor exchange interaction is introduced and investigated using the standard methods of statistical mechanics. Besides of the volume-dependent magnetic energy, the static electromagnetic energy and anharmonic Einstein phonon contribution are also taken into account. Taking the simple volume dependence of all energy contributions we have obtained the equation of state, magnetic moment, internal and Helmholtz free energy of the system. The ground-state and finite-temperature phase diagrams are obtained and discussed in detail. Is it shown that the generalized spin-1 Blume–Capel model exhibits a novel critical behavior appearing due to magnetostriction and thermal volume variations. The presented approach is very universal and easily applicable to many other theoretical models in different fields of solid state physics.

Alternative Structures of α-Synuclein.

The object of our analysis is the structure of alpha-synuclein (ASyn), which, under in vivo conditions, associates with presynaptic vesicles. Misfolding of ASyn is known to be implicated in Parkinson’s disease. The availability of structural information for both the micelle-bound and amyloid form of ASyn enables us to speculate on the specific mechanism of amyloid transformation. This analysis is all the more interesting given the fact that—Unlike in Aβ(1–42) amyloids—only the central fragment (30–100) of ASyn has a fibrillar structure, whereas, its N- and C-terminal fragments (1–30 and 100–140, respectively) are described as random coils. Our work addresses the following question: Can the ASyn chain—as well as the aforementioned individual fragments—adopt globular conformations? In order to provide an answer, we subjected the corresponding sequences to simulations carried out using Robetta and I-Tasser, both of which are regarded as accurate protein structure predictors. In addition, we also applied the fuzzy oil drop (FOD) model, which, in addition to optimizing the protein’s internal free energy, acknowledges the presence of an external force field contributed by the aqueous solvent. This field directs hydrophobic residues to congregate near the center of the protein body while exposing hydrophilic residues on its surface. Comparative analysis of the obtained models suggests that fragments which do not participate in forming the amyloid fibril (i.e., 1–30 and 100–140) can indeed attain globular conformations. We also explain the influence of mutations observed in vivo upon the susceptibility of ASyn to undergo amyloid transformation. In particular, the 30–100 fragment (which adopts a fibrillar structure in PDB) is not predicted to produce a centralized hydrophobic core by any of the applied toolkits (Robetta, I-Tasser, and FOD). This means that in order to minimize the entropically disadvantageous contact between hydrophobic residues and the polar solvent, ASyn adopts the form of a ribbonlike micelle (rather than a spherical one). In other words, the ribbonlike micelle represents a synergy between the conformational preferences of the protein chain and the influence of its environment.

Continuum mechanics for thermo-chemo-mechanical coupling system based on decomposition of internal energy

In this paper, based on the decomposition of internal energy into free internal energy and dissipative energy, some conservation laws of a thermodynamically open continuum system as well as related constitutive relations and evolution equations are derived when considering heat conduction, mass transfusion, chemical reactant and mechanical deformation. Upon establishing a weak form of corresponding governing differential equations and boundary conditions under above theoretical framework, a simple example is then numerically implemented to demonstrate the solution procedure.

Coupled thermoelastic theory and associated variational principles based on decomposition of internal energy

A new framework of coupled thermoelasticity is constructed in this paper based on a decomposition of internal energy into free internal energy and dissipative energy. Fundamental equations (i.e. divergence and gradient equations, constitutive equations including evolving laws) along with proper boundary conditions are all included in this framework, from which two novel dual-complementary variational principles with explicit functionals are proposed. Unlike the conventional thermoelastic theory, the proposed variational principles for thermoelasticity are established without the approximate assumption of small temperature changes. To verify the usefulness of the proposed variational principles in simulating coupled thermoelastic problems, a coupled thermoelastic example is numerically implemented.