How the Brain Becomes the Mind: Can Thermodynamics Explain the Emergence and Nature of Emotions?

The neural systems’ electric activities are fundamental for the phenomenology of consciousness. Sensory perception triggers an information/energy exchange with the environment, but the brain’s recurrent activations maintain a resting state with constant parameters. Therefore, perception forms a closed thermodynamic cycle. In physics, the Carnot engine is an ideal thermodynamic cycle that converts heat from a hot reservoir into work, or inversely, requires work to transfer heat from a low- to a high-temperature reservoir (the reversed Carnot cycle). We analyze the high entropy brain by the endothermic reversed Carnot cycle. Its irreversible activations provide temporal directionality for future orientation. A flexible transfer between neural states inspires openness and creativity. In contrast, the low entropy resting state parallels reversible activations, which impose past focus via repetitive thinking, remorse, and regret. The exothermic Carnot cycle degrades mental energy. Therefore, the brain’s energy/information balance formulates motivation, sensed as position or negative emotions. Our work provides an analytical perspective of positive and negative emotions and spontaneous behavior from the free energy principle. Furthermore, electrical activities, thoughts, and beliefs lend themselves to a temporal organization, an orthogonal condition to physical systems. Here, we suggest that an experimental validation of the thermodynamic origin of emotions might inspire better treatment options for mental diseases.     

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties

Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius’ virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law’s evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.     

Heat Transfer and Pressure Drop of Nanofluid with Rod-like Particles in Turbulent Flows through a Curved Pipe

Pressure drop, heat transfer, and energy performance of ZnO/water nanofluid with rodlike particles flowing through a curved pipe are studied in the range of Reynolds number 5000 ≤ Re ≤ 30,000, particle volume concentration 0.1% ≤ Φ ≤ 5%, Schmidt number 10⁴ ≤ Sc ≤ 3 × 10⁵, particle aspect ratio 2 ≤ λ ≤ 14, and Dean number 5 × 10³ ≤ De ≤ 1.5 × 10⁴. The momentum and energy equations of nanofluid, together with the equation of particle number density for particles, are solved numerically. Some results are validated by comparing with the experimental results. The effect of Re, Φ, Sc, λ, and De on the friction factor f and Nusselt number Nu is analyzed. The results showed that the values of f are increased with increases in Φ, Sc, and De, and with decreases in Re and λ. The heat transfer performance is enhanced with increases in Re, Φ, λ, and De, and with decreases in Sc. The ratio of energy PEC for nanofluid to base fluid is increased with increases in Re, Φ, λ, and De, and with decreases in Sc. Finally, the formula of ratio of energy PEC for nanofluid to base fluid as a function of Re, Φ, Sc, λ, and De is derived based on the numerical data.     

Numerical Investigation of Heat Transfer Characteristics of scCO2 Flowing in a Vertically-Upward Tube with High Mass Flux

In this work, the heat transfer characteristics of supercritical pressure CO₂ in vertical heating tube with 10 mm inner diameter under high mass flux were investigated by using an SST k-ω turbulent model. The influences of inlet temperature, heat flux, mass flux, buoyancy and flow acceleration on the heat transfer of supercritical pressure CO₂ were discussed. Our results show that the buoyancy and flow acceleration effect based on single phase fluid assumption fail to explain the current simulation results. Here, supercritical pseudo-boiling theory is introduced to deal with heat transfer of scCO₂. scCO₂ is treated to have a heterogeneous structure consisting of vapor-like fluid and liquid-like fluid. A physical model of scCO₂ heat transfer in vertical heating tube was established containing a gas-like layer near the wall and a liquid-like fluid layer. Detailed distribution of thermophysical properties and turbulence in radial direction show that scCO₂ heat transfer is greatly affected by the thickness of gas-like film, thermal properties of gas-like film and turbulent kinetic energy in the near-wall region. Buoyancy parameters Bu < 10⁻⁵, Bu* < 5.6 × 10⁻⁷ and flow acceleration parameter K_v < 3 × 10⁻⁶ in this paper, which indicate that buoyancy effect and flow acceleration effect has no influence on heat transfer of scCO₂ under high mass fluxes. This work successfully explains the heat transfer mechanism of supercritical fluid under high mass flux.     

Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials

The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and χ2 distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes’ maximal entropy priors are formally expressed in terms of the empirical densities’ entropic convex duals. Expanding these duals on orthogonal polynomial bases allows for the expedient determination of the Jaynes–Gibbs priors. Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor’s orthogonal polynomial expansion coefficients in random variable space. Genomics and geophysics examples are provided.     

Economic Cycles of Carnot Type

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a Q−P diagram and a E−I diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential.     

Using a Partially Evaporating Cycle to Improve the Volume Ratio Problem of the Trilateral Flash Cycle for Low-Grade Heat Recovery

This study examined the trilateral flash cycle characteristics (TFC) and partially evaporating cycle (PEC) using a low-grade heat source at 80 °C. The evaporation temperature and mass flow rate of the working fluids and the expander inlet’s quality were optimized through pinch point observation. This can help advance methods in determining the best design points and their operating conditions. The results indicated the partially evaporating cycle could solve the high-volume ratio problem without sacrificing the net power and thermal efficiency performance. When the system operation’s saturation temperature decreased by 10 °C, the net power, thermal efficiency, and volume ratio of the trilateral flash cycle system decreased by approximately 20%. Conversely, with the same operational conditions, the net power and thermal efficiency of the partially evaporating cycle system decreased by only approximately 3%; however, the volume ratio decreased by more than 50%. When the system operating temperature was under 63 °C, each fluid’s volume ratio could decrease to approximately 5. The problem of high excessive expansion would be solved from the features of the partially evaporating cycle, and it will keep the ideal power generation efficiency and improve expander manufacturing.     

The Carnot Cycle,Reversibility and Entropy

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally.     

A Generalization of the Concavity of Rényi Entropy Power

Recently, Savaré-Toscani proved that the Rényi entropy power of general probability densities solving the p-nonlinear heat equation in Rn is a concave function of time under certain conditions of three parameters n,p,μ , which extends Costa’s concavity inequality for Shannon’s entropy power to the Rényi entropy power. In this paper, we give a condition Φ(n,p,μ) of n,p,μ under which the concavity of the Rényi entropy power is valid. The condition Φ(n,p,μ) contains Savaré-Toscani’s condition as a special case and much more cases. Precisely, the points (n,p,μ) satisfying Savaré-Toscani’s condition consist of a two-dimensional subset of R3 , and the points satisfying the condition Φ(n,p,μ) consist a three-dimensional subset of R3 . Furthermore, Φ(n,p,μ) gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach.     

Differential temperature Carnot heat analysis shows that computing machines are thermodynamically irreversible

We perform a differential temperature Carnot analysis of the changes in energy and entropy (degrees of freedom) associated with an ideal classical computing machine. Assuming that Carnot’s maximum efficiency law is as equally applicable to a computing machine as to a mechanical machine, we find that useful computation is necessarily dissipative and thermodynamically irreversible. In addition, we find that copying or cloning of information is as dissipative as the original process employed to create the information (through a computation) in the first place. We prove minimum heat dissipation kT ln 2 per output calculation bit, where T is the thermodynamic temperature of unavoidable by-product bits (i.e. not the output calculation bits) rather than a generally assumed ‘surrounding environment’ temperature. Overall, this places computers into the same category as conventional machines, obeying the second law of thermodynamics and always operating below 100% efficiency, such that a perpetual calculating machine cannot exist.     

Effects of Tau and Sampling Frequency on the Regularity Analysis of ECG and EEG Signals Using ApEn and SampEn Entropy Estimators

Electrocardiography (ECG) and electroencephalography (EEG) signals provide clinical information relevant to determine a patient’s health status. The nonlinear analysis of ECG and EEG signals allows for discovering characteristics that could not be found with traditional methods based on amplitude and frequency. Approximate entropy (ApEn) and sampling entropy (SampEn) are nonlinear data analysis algorithms that measure the data’s regularity, and these are used to classify different electrophysiological signals as normal or pathological. Entropy calculation requires setting the parameters r (tolerance threshold), m (immersion dimension), and τ (time delay), with the last one being related to how the time series is downsampled. In this study, we showed the dependence of ApEn and SampEn on different values of τ, for ECG and EEG signals with different sampling frequencies (F_s), extracted from a digital repository. We considered four values of F_s (128, 256, 384, and 512 Hz for the ECG signals, and 160, 320, 480, and 640 Hz for the EEG signals) and five values of τ (from 1 to 5). We performed parametric and nonparametric statistical tests to confirm that the groups of normal and pathological ECG and EEG signals were significantly different (p < 0.05) for each F and τ value. The separation between the entropy values of regular and irregular signals was variable, demonstrating the dependence of ApEn and SampEn with F_s and τ. For ECG signals, the separation between the conditions was more robust when using SampEn, the lowest value of F_s, and τ larger than 1. For EEG signals, the separation between the conditions was more robust when using SampEn with large values of F_s and τ larger than 1. Therefore, adjusting τ may be convenient for signals that were acquired with different F_s to ensure a reliable clinical classification. Furthermore, it is useful to set τ to values larger than 1 to reduce the computational cost.     

Statistical Inference for Ergodic Algorithmic Model (EAM), Applied to Hydrophobic Hydration Processes

The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Thermal Partition Function {T-PF}. By development of {DS-PF}, parabolic binding potential functions α) RlnK_dual = (−ΔG°_dual/T) ={f(1/T)*g(T)} and β) RTlnK_dual = (−ΔG°_dual) = {f(T)*g(lnT)} have been calculated. The resulting binding functions are “convoluted” functions dependent on the reciprocal interactions between the primary function f(1/T) or f(T) with the secondary function g(T) or g(lnT), respectively. The binding potential functions carry the essential thermodynamic information elements of each system. The analysis of the binding potential functions experimentally determined at different temperatures by means of the Thermal Equivalent Dilution (TED) principle has made possible the evaluation, for each compound, of the pseudo-stoichiometric coefficient ±ξ_w, from the curvature of the binding potential functions. The positive value indicates convex binding functions (Class A), whereas the negative value indicates concave binding function (Class B). All the information elements concern sets of compounds that are very different from one set to another, in molecular dimension, in chemical function, and in aggregation state. Notwithstanding the differences between, surprising equal unitary values of niche (cavity) formation in Class A <Δh_for>_A = −22.7 ± 0.7 kJ·mol⁻¹ ·ξ_w⁻¹ sets with standard deviation σ = ±3.1% and <Δs_for>_A = −445 ± 3J·K⁻¹·mol⁻¹·ξ_w⁻¹J·K⁻¹·mol⁻¹·ξ_w⁻¹ with standard deviation σ = ±0.7%. Other surprising similarities have been found, demonstrating that all the data analyzed belong to the same normal statistical population. The Ergodic Algorithmic Model (EAM) has been applied to the analysis of important classes of reactions, such as thermal and chemical denaturation, denaturation of proteins, iceberg formation or reduction, hydrophobic bonding, and null thermal free energy. The statistical analysis of errors has shown that EAM has a general validity, well beyond the limits of our experiments. Specifically, the properties of hydrophobic hydration processes as biphasic systems generating convoluted binding potential functions, with water as the implicit solvent, hold for all biochemical and biological solutions, on the ground that they also are necessarily diluted solutions, statistically validated.     

Heat Transfer and Fluid Flow Characteristics of Microchannel with Oval-Shaped Micro Pin Fins

A novel microchannel heat sink with oval-shaped micro pin fins (MOPF) is proposed and the characteristics of fluid flow and heat transfer are studied numerically for Reynolds number (Re) ranging from 157 to 668. In order to study the influence of geometry on flow and heat transfer characteristics, three non-dimensional variables are defined, such as the fin axial length ratio (α), width ratio (β), and height ratio (γ). The thermal enhancement factor (η) is adopted as an evaluation criterion to evaluate the best comprehensive thermal-hydraulic performance of MOPF. Results indicate that the oval-shaped pin fins in the microchannel can effectively prevent the rise of heat surface temperature along the flow direction, which improves the temperature distribution uniformity. In addition, results show that for the studied Reynolds number range and microchannel geometries in this paper, the thermal enhancement factor η increases firstly and then decreases with the increase of α and β. In addition, except for Re = 157, η decreases first and then increases with the increase of the fin height ratio γ. The thermal enhancement factor for MOPF with α = 4, β = 0.3, and γ = 0.5 achieves 1.56 at Re = 668. The results can provide a theoretical basis for the design of a microchannel heat exchanger.     

When,why, and how does like like like?: Electrostatic attraction between similarly charged species

In the Derjaguin-Landau-Verwey-Overbeek (DLVO) framework of the past 60 years, colloidal interaction between similarly charged particles has been claimed to be simply repulsive, and an attraction such as the van der Waals interaction is attached to the Coulombic repulsion. Statistical-thermodynamic considerations show that the electrostatic Helmholtz free energy ΔF^el is generally not equal to the electrostatic Gibbs free energy ΔG^el for simple ionic solutions, and the difference ΔG^el–ΔF^el (corresponding to the electrostatic osmotic pressure p^el) becomes larger with increasing charge number. Thus, it is expected that ΔG^el–ΔF^el be large for highly charged macroions. In the DLVO framework, however, ΔG^el = ΔF^el was postulated. Sogami showed that a mean field approach reproduced repulsion at the level of ΔF^el but resulted in (repulsion and) attraction at the level of ΔG^el. Overbeek’s critique of Sogami theory is shown to be in error. If this criticism were correct, then not only the Sogami theory but also the Debye-Hückel theory would be wrong. The attraction is thus confirmed to exist not only for multi-valent but also mono-valent counterions.     

(火积)理论在热功转换过程中的应用探讨

分析和讨论了(火积)理论在热功转换过程的应用及其局限性.对Carnot循环的分析表明,Carnot循环中系统的(火积)是平衡的,但(火积)和熵之间不存在dG=T2dS这样的联系.对于一般热力学过程,分析表明,在热量传递到内可逆循环中间接对外做功时,现有的(火积)理论可用于系统的分析.讨论了热功转换过程分析中(火积)理论与熵理论的不同.分析表明,两个理论的分析角度及优化输出功的前提条件是不同的.熵产从可用能损失的角度分析热功转换过程,而(火积)理论则从热量势能消耗的角度.当输入系统的可用能给定或者输入系统的热量及热量进、出系统的热力学力给定时,熵产最小化对应于输出功最大;对于(火积)理论,则当输入系统的热量及热量进、出系统的温度给定时,最大(火积)损失对应于最大输出功.同时,它们各自均有局限性.当相应的前提条件不满足时,最大(火积)损失或最小熵产可能不与最大输出功相对应.     

Rényi Entropy and Free Energy

The Rényi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Rényi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide the temperature by q. Then the maximum amount of work the system can perform as it moves to equilibrium at the new temperature divided by the change in temperature equals the system’s Rényi entropy in its original state. This result applies to both classical and quantum systems. Mathematically, we can express this result as follows: the Rényi entropy of a system in thermal equilibrium is without the ‘q−1-derivative’ of its free energy with respect to the temperature. This shows that Rényi entropy is a q-deformation of the usual concept of entropy.     

Electroosmosis-Optimized Thermal Model for Peristaltic Transportation of Thermally Radiative Magnetized Liquid with Nonlinear Convection

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength.     

Information Dark Energy Can Resolve the Hubble Tension and Is Falsifiable by Experiment

We consider the role information energy can play as a source of dark energy. Firstly, we note that if stars and structure had not formed in the universe, elemental bits of information describing the attributes of particles would have exhibited properties similar to the cosmological constant. The Landauer equivalent energy of such elemental bits would be defined in form and value identical to the characteristic energy of the cosmological constant. However, with the formation of stars and structure, stellar heated gas and dust now provide the dominant contribution to information energy with the characteristics of a dynamic, transitional, dark energy. At low redshift, z < ~1.35, this dark energy emulates the cosmological constant with a near-constant energy density, w = −1.03 ± 0.05, and an energy total similar to the mc² of the universe’s ∼10⁵³ kg of baryons. At earlier times, z > ~1.35, information energy was phantom, differing from the cosmological constant, Λ, with a CPL parameter difference of ∆w_o = −0.03 ± 0.05 and ∆w_a = −0.79 ± 0.08, values sufficient to account for the H₀ tension. Information dark energy agrees with most phenomena as well as Λ, while exhibiting characteristics that resolve many tensions and problems of ΛCDM: the cosmological constant problem; the cosmological coincidence problem; the H₀ tension, and the σ₈ tension. As this proposed dark energy source is not usually considered, we identify the expected signature in H(a) that will enable the role of information dark energy to be falsified by experimental observation.     

Chemistry of a novel zerovalent ruthenium π-acidic alkene complex,Ru (η6-1,3,5-cyclooctatriene)(η2-dimethyl fumarate)2

A novel zerovalent ruthenium complex with a π-acidic ligand, Ru(η⁶-cyclooctatriene)(η²-dimethyl fumarate)₂ (1), was prepared from Ru(η⁴-cyclooctadiene)(η⁶-cyclooctatriene) [Ru(cod)(cot)]. Complex 1 or Ru(cod)(cot) catalyzes various new carbon-carbon bond-forming reactions that include the [2 + 2] cycloaddition of alkenes and alkynes via ruthenacycles, the creation of a new hydrocarbon, pentacyclo[6.6.0.0^2,6.0^3,13.0^10,14]tetradeca-4,11-diene [PCTD], by dimerization of 2,5-norbornadiene via C-C bond cleavage, and the codimerization of alkynes and/or alkenes. Complex 1 was shown to be an excellent mother complex for various zerovalent ruthenium complexes. Complex 1 reacts with amines, phosphines or water to give new zerovalent ruthenium complexes with the ligands. The resulting aqua complexes have a water ligand with an oxygen atom that is a chiral center, i.e., ruthenium complexes with a ‘chiral water’ ligand were prepared and fully characterized.     

Thermodynamic Properties of the First-Generation Hybrid Dendrimer with “Carbosilane Core/Phenylene Shell” Structure

The molar heat capacity of the first-generation hybrid dendrimer with a “carbosilane core/phenylene shell” structure was measured for the first time in the temperature range T = 6–600 K using a precise adiabatic vacuum calorimeter and DSC. In the above temperature interval, the glass transition of the studied compound was observed, and its thermodynamic characteristics were determined. The standard thermodynamic functions (the enthalpy, the entropy, and the Gibbs energy) of the hybrid dendrimer were calculated over the range from T = 0 to 600 K using the experimentally determined heat capacity. The standard entropy of formation of the investigated dendrimer was evaluated at T = 298.15 K. The obtained thermodynamic properties of the studied hybrid dendrimer were compared and discussed with the literature data for some of the first-generation organosilicon and pyridylphenylene dendrimers.