Hydrogen isotope population near dislocations in zirconium from molecular dynamics.

Performance of zirconium tritides used for hydrogen isotope storage is significantly changed under reactor environments. This can be attributed to the formation of various radiation-induced dislocations. To help gain insight, molecular dynamics simulations have been employed to investigate hydrogen isotope population in zirconium containing different types of edge dislocations. Our studies reveal that hydrogen isotope concentration is highest near the tensile side of dislocation cores and varies based on dislocation type. This increase in hydrogen isotope concentration can be explained by the Boltzmann equation based on calculations using swelling volume and pressure field, with significantly reduced computational cost. Strikingly, because hydrogen isotope in the compressive regions of dislocations is depleted, the overall hydrogen isotope content is found to be unchanged by dislocation formation. These results counter the previous view that the dislocation trapping effect increases hydrogen isotope solubility and provide an understanding of changes in hydrogen isotope pressure under reactor conditions. By elucidating the impact of dislocations on hydrogen isotope storage performance, this research offers insights for optimizing zirconium tritides in nuclear applications. and contributes to the advancement of hydrogen isotope storage materials.

In Situ Induced Interface Engineering in Hierarchical Fe3O4 Enhances Performance for Alkaline Solid-State Energy Storage.

Rechargeable aqueous batteries adopting Fe-based materials are attracting widespread attention by virtue of high-safety and low-cost. However, the present Fe-based anodes suffer from low electronic/ionic conductivity and unsatisfactory comprehensive performance, which greatly restrict their practicability. Concerning the principle of physical chemistry, fabricating electrodes that could simultaneously achieve ideal thermodynamics and fast kinetics is a promising issue. Herein, hierarchical Fe3O4@Fe foam electrode with enhanced interface/grain boundary engineering is fabricated through an in situ self-regulated strategy. The electrode achieves ultrahigh areal capacity of 31.45 mA h cm-2 (50 mA cm-2), good scale application potential (742.54 mA h for 25 cm2 electrode), satisfied antifluctuation capability, and excellent cycling stability. In/ex situ characterizations further validate the desired thermodynamic and kinetic properties of the electrode endowed with accurate interface regulation, which accounts for salient electrochemical reversibility in a two-stage phase transition and slight energy loss. This work offers a suitable strategy in designing high-performance Fe-based electrodes with comprehensive inherent characteristics for high-safety large-scale energy storage.

Electricity-driven dealkalization of bauxite residue based on thermodynamics, kinetics, and mineral transformation.

High alkalinity content of bauxite residue is a major factor that hinders resource reutilization and pollutes the environment. Although acid neutralization is a direct and effective method, the amount of acid and secondary waste of sodium salt are still difficult problems to solve. Herein, we innovatively integrated an electric field into the acid neutralization dealkalization of bauxite residue and analyzed the dealkalization behavior by thermodynamics, kinetics, and mineral transformation. The results show that the pH of the anode chamber was maintained at the acidic levels of 3-6 after 30 min of galvanostatic electrolysis, and bauxite residue can realize dealkalization by acid neutralization. In the anode chamber, Na+ was released into the leachate via the reactions of Na3Al3Si3O12 and the removal of encapsulated soluble alkali. The stainless steel wire mesh anode exhibited its superiority and decreased the Na2O content in bauxite residue from 9.48 to 3.13% through convective mass transfer driven by the electric field and steady-state diffusion under stirring. This research provides a promising method for the electricity-driven dealkalization of bauxite residue, thus facilitating the development of multifield coupling theory and the application of electric fields in the alumina industry.

Towards rapid formation of electroactive biofilm: insights from thermodynamics and electric field manipulation.

Electroactive biofilm (EAB) has garnered significant attention due to its effectiveness in pollutant remediation, electricity generation, and chemical synthesis. However, achieving precise control over the rapid formation of EAB presents challenges for the practical implementation of bioelectrochemical technology. In this study, we investigated the regulation of EAB formation by manipulating applied electric potential. We developed a modified XDLVO model for the applied electric field and quantitatively assessed the feasibility of existing rapid formation strategies for EAB. Our results revealed that electrostatic (EL) force significantly influenced EAB formation in the presence of the applied electric field, with the potential difference between the electrode and the microbial solution being the primary determinant of EL force. Compared to -0.2 V and 0 V vs.Ag/AgCl, EAB exhibited the highest electrochemical performance at 0.2 V vs.Ag/AgCl, with a maximum current density of 6.044 ± 0.10 A/m2, surpassing that at -0.2 V vs.Ag/AgCl and 0 V vs.Ag/AgCl by 1.73 times and 1.31 times, respectively. Furthermore, EAB demonstrated the highest biomass accumulation, measuring a thickness of 25 ± 2 µm at 0.2 V vs. Ag/AgCl, representing increases of 1.67 and 1.25 times compared to -0.2 V vs.Ag/AgCl and 0 V vs.Ag/AgCl, respectively. The strong electrostatic attraction under the anodic potential promoted the formation of a monolayer of biofilm. Additionally, the hydrophilicity and hydrophobicity of the biofilm were altered following inversion culture. The Lewis acid-base (AB) attraction offset the electrostatic repulsion caused by negative charges, it is beneficial for the formation of biofilms. This study, for the first time, elucidated the difference in the formation of cathode and anode biofilm from a thermodynamic perspective in the context of electric field introduction, laying the theoretical foundation for the directional regulation of the rapid formation of typical electroactive biofilms.

A sustainable and economical solution for CO2 capture with biobased carbon materials derived from palm kernel shells.

This study investigates the synthesize of activated carbon for carbon dioxide adsorption using palm kernel shell (PKS), a by-product of oil palm industry. The adsorbent synthesis involved a simple two-step carbonization method. Firstly, PKS was activated with potassium oxide (KOH), followed by functionalization with magnesium oxide (MgO). Surface analysis revealed that KOH activated PKS has resulted in a high specific surface area of 1086 m2/g compared to untreated PKS (435 m2/g). However, impregnation of MgO resulted in the reduction of surface area due to blockage of pores by MgO. Thermogravimetric analysis (TGA) demonstrated that PKS-based adsorbents exhibited minimal weight loss of less than 30% up to 500 °C, indicating their suitability for high-temperature applications. CO2 adsorption experiments revealed that PKS-AC-MgO has achieved a higher adsorption capacity of 155.35 mg/g compared to PKS-AC (149.63 mg/g) at 25 °C and 5 bars. The adsorption behaviour of PKS-AC-MgO was well fitted by both the Sips and Langmuir isotherms, suggesting a combination of both heterogeneous and homogeneous adsorption and indicating a chemical reaction between MgO and CO2. Thermodynamic analysis indicated a spontaneous and thermodynamically favourable process for CO2 capture by PKS-AC-MgO, with negative change in enthalpy (- 0.21 kJ/mol), positive change in entropy (2.44 kJ/mol), and negative change in Gibbs free energy (- 729.61 J/mol, - 790.79 J/mol, and - 851.98 J/mol) across tested temperature. Economic assessment revealed that the cost of PKS-AC-MgO is 21% lower than the current market price of commercial activated carbon, indicating its potential for industrial application. Environmental assessment shows a significant reduction in greenhouse gas emissions (381.9 tCO2) through the utilization of PKS-AC-MgO, underscoring its environmental benefits. In summary, the use of activated carbon produced from PKS and functionalised with MgO shows great potential for absorbing CO2. This aligns with the ideas of a circular economy and sustainable development.

Has the human biological interaction with SARS-CoV2 variants entered a pliant "Faustian bargain"?

We hypothesize that a "Faustian bargain"-the trading of increased SARS-CoV2 viral infection with a concurrent potential for prevention of life-threatening lower lung infection explains the previous and future morbidity and mortality from COVID-19. Further, this trade-off is made feasible by fundamental principles of thermodynamics and receptor affinity.

Synergistic adsorption of methylene blue using ternary composite of phosphoric acid geopolymer, calcium alginate, and sodium lauryl sulfate.

The removal of dyes from the aquatic ecosystem is necessary being a major threat to life. For enhanced remediation of methylene blue (MB) dye, a new ternary biopolymer-geopolymer-surfactant composite adsorbent is synthesized by combining phosphoric acid geopolymer (PAGP), calcium alginate (Alg), and sodium lauryl sulfate (SLS). During the synthesis of the composites, PAGP and SLS were mixed with the alginate matrix, producing porous hybrid beads. The PAGP-SLS-alginate (PSA) beads prepared were characterized using different analytical tools, i.e., scanning electron microscopy (SEM), Fourier transform infrared spectrophotometry (FTIR), X-ray diffractometry (XRD), surface area and porosimetery (SAP), and thermogravimetric analysis (TGA). To ascertain the ideal conditions for the adsorption process, a batch reactor procedure was used to investigate the effects of several parameters on MB adsorption, including pH (2, 4, 6, 8, 10), PSA adsorbent dosage (0.06-0.12 g), MB concentration (50-500 mg/L), contact time (15 to 300 min), and temperature (25, 35, and 45 °C). The SEM investigation indicated that ~ 1860 µm-sized PSA beads with 6-8 µm voids are generated. Based on XRD, FTIR, and SAP examinations, the material is amorphous, having numerous functional groups and an average pore size of 6.42 nm. Variation of pH has a little effect on the adsorption process, and the pH of 7.44 was found to be the pHpzc of the PSA beads. According to the findings of the batch study, equilibrium adsorption was obtained in 270-300 min, showing that the adsorption process was moderately slow-moving and effective. The dye adsorption linearly increased with initial dye concentration over concentration range of 50-500 mg/L and reciprocally decreased with rise in temperature. 0.06 g adsorbent dose, 25 °C, pH10, and 270 min were found to be the better conditions for adsorption experiments. Langmuir isotherm fitted well compared to Freundlich, Temkin, and Dubinin-Radushkevich (DR) isotherm models on the experimental data, and the maximum adsorption capacity(qmax) calculated was 1666.6 mg. g-1. Pseudo-second-order (PSO) kinetics model and multi steps (two) intra particle diffusion (IPD) model fitted well on the adsorption kinetics data. The system's entropy, Gibbs free energy, and change in enthalpy were measured and found to be -109.171 J. mol-1. K-1, - 8.198 to - 6.014 kJ. mol-1, and - 40.747 kJ. mol-1. Thermodynamics study revealed that adsorption process is exothermic, energetically favorable and resulting in the decrease in randomness. Chemisorption is found to be the dominant mechanism as confirmed by pH effect, Langmuir isotherm, PSO kinetics, IPD model, and thermodynamics parameters. PSA beads were successfully regenerated using ethanol in a course of 120 min and re-used for five times. To sum up, the PSA adsorbent's impressive adsorption capability of 1666.66 mg/g highlights its potential as a successful solution for methylene blue removal. The results of this study add to the expanding corpus of information on sophisticated adsorption materials and demonstrate PSA's potential for real-world uses in wastewater treatment and environmental clean-up.

Comprehensive batch studies on removal of fluoride from aqueous solution by acid and alkali-activated adsorbents prepared from Dal lake weeds: Mechanism, Kinetics and Thermodynamics.

An efficient and economical way of eliminating fluoride from water is being investigated by employing the buoyant aquatic plant (Dal weed). Two post-pyrolysis chemical activation alteration techniques were implemented: acidic activation by employing sulfuric acid (H-activation) and alkaline activation using sodium hydroxide (OH-activation). The batch kinetic studies have been carried out considering varying starting fluoride levels such as 2-10 mg/L. The impact of diverse procedural factors, including dosage of Dal weed, starting fluoride level, pH and contact duration was observed to determine their influence on fluoride adsorption kinetics. Based on analyzed exploratory results, removal efficacy of 63% for the OH-activated carbon and 83% for H-activated carbon was achieved at commencing fluoride level of 10 mg/L, adsorbent dosage of 0.8 g, at 25 °C after 120 min. The maximal fluoride uptake capacity for H-activated carbon was observed to be 78.158 mg/g. Kinetic investigations showed that the Freundlich isotherm model provided a satisfactory match with an R2 value of 0.99. The reaction order nature adhered to kinetics resembling pseudo second order. Thermodynamic investigation revealed endothermic sorption, with negative ΔG indicating spontaneous fluoride uptake. In comparison, the positive number for ΔS suggested random behavior at the contact involving the adsorbent and adsorbate. The investigations into the regeneration capabilities of the adsorbent material revealed that even after undergoing for five consecutive cycles of adsorption and regeneration, the adsorbent exhibited an uptake potential of 45%. The presence of competing ions in the solution negatively impacted defluoridation efficacy, with the influence following the order of HCO3-< NO3-< Cl-< SO42-< PO43-.

From X-ray crystallographic structure to intrinsic thermodynamics of protein-ligand binding using carbonic anhydrase isozymes as a model system.

Carbonic anhydrase (CA) was among the first proteins whose X-ray crystal structure was solved to atomic resolution. CA proteins have essentially the same fold and similar active centers that differ in only several amino acids. Primary sulfonamides are well defined, strong and specific binders of CA. However, minor variations in chemical structure can significantly alter their binding properties. Over 1000 sulfonamides have been designed, synthesized and evaluated to understand the correlations between the structure and thermodynamics of their binding to the human CA isozyme family. Compound binding was determined by several binding assays: fluorescence-based thermal shift assay, stopped-flow enzyme activity inhibition assay, isothermal titration calorimetry and competition assay for enzyme expressed on cancer cell surfaces. All assays have advantages and limitations but are necessary for deeper characterization of these protein-ligand interactions. Here, the concept and importance of intrinsic binding thermodynamics is emphasized and the role of structure-thermodynamics correlations for the novel inhibitors of CA IX is discussed - an isozyme that is overexpressed in solid hypoxic tumors, and thus these inhibitors may serve as anticancer drugs. The abundant structural and thermodynamic data are assembled into the Protein-Ligand Binding Database to understand general protein-ligand recognition principles that could be used in drug discovery.

Magnetic bio-composite based on zirconium and chitosan modified activated carbon from peanut husk with enhanced antibacterial and adsorptive potential for alizarin red and congo red in wastewater.

Creating new adsorbents is crucial for removing contaminants from water due to increased industrialization, which has worsened water pollution in recent years. In this study, a magnetic biocomposite, Zirconium (Zr)-doped chitosan (CS)-coated iron oxide nanoparticles (Fe3O4-NPs)-peanut husk (PH)-based activated carbon (AC) (Zr-CS/Fe3O4-NPs@PH-AC), was synthesized for efficient removal of alizarin red (AR) and congo red (CR) dyes, alongside antibacterial applications. Characterization via scanning electron microscopy (SEM) and Brunauer-Emmett-Teller (BET) analysis revealed micropores and mesopores development due to chemical activation of PH biomaterial and Fe3O4-NPs addition. Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD) identified functional groups and structural properties. Vibrating sample magnetometry (VSM) analyzed magnetic properties. Optimal conditions for AR/CR removal were determined, including Zr-CS/Fe3O4-NPs@PH-AC dose, dye dose, contact time, and temperature, achieving maximum removal percentages. Experimentally determined maximum adsorption capacities for AR and CR were 374.3 and 154.1 mg·g-1, respectively. Cytotoxicity studies affirmed the eco-friendly and non-toxic nature of the adsorbent by exhibiting the reduction in the cell viability from 100 % to 88.68 % from the 0 to 200 µg·L-1 respectively. Additionally, the biocomposite exhibited significant antibacterial activity against Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) due to magnetic NPs. The material in this study shows extreme compatibility for numerous applications.

Understanding the Thermodynamics of Magnesium Binding to RNA Structural Motifs.

Divalent magnesium ions (Mg2+) serve a vital role in defining the structural and catalytic chemistry of a wide array of RNA molecules. The body of structural information on RNA motifs continues to expand and, in turn, the functional importance of Mg2+ is revealed. A combination of prior work on the structural characterization of magnesium binding ligands with inner- and outer-sphere coordination modes, with recorded experimental binding energies for inner- and outer-sphere contacts, demonstrates the relative affinity and thermodynamic hierarchy for these sites. In turn, these can be correlated with cellular concentrations of free available magnesium ions, allowing the prioritization of populating important functional sites and a correlation with physiological function. This paper summarizes some of the key results of that analysis and provides predictive rules for the affinity and role of newly identified Mg binding sites on complex RNA structures. The influence of crystal packing on magnesium binding to RNA motifs, relative to their solution form, is addressed and caveats made.

Thermodynamic Analysis of n-Nonadecane (C19H40)/1-Octadecanol (C18H37OH) Blends.

The article delves into the intricate phase transitions of 1-Octadecanol and n-Nonadecane within a binary system, unveiling dynamic structural changes under varying conditions. Through Fourier transform infrared (FTIR) analysis, specific molecular vibrations were identified, shedding light on the molecular composition and interactions. The study highlights the challenges in detecting subtle phase transitions and emphasises the individuality of molecular behaviours in closely related compounds. The findings underscore the complexity of phase transitions in binary systems and advocate for a nuanced approach to studying molecular structures and behaviours.

Rebuilding the Habitable Zone from the Bottom up with Computational Zones.

Computation, if treated as a set of physical processes that act on information represented by states of matter, encompasses biological systems, digital systems, and other constructs and may be a fundamental measure of living systems. The opportunity for biological computation, represented in the propagation and selection-driven evolution of information-carrying organic molecular structures, has been partially characterized in terms of planetary habitable zones (HZs) based on primary conditions such as temperature and the presence of liquid water. A generalization of this concept to computational zones (CZs) is proposed, with constraints set by three principal characteristics: capacity (including computation rates), energy, and instantiation (or substrate, including spatial extent). CZs naturally combine traditional habitability factors, including those associated with biological function that incorporate the chemical milieu, constraints on nutrients and free energy, as well as element availability. Two example applications are presented by examining the fundamental thermodynamic work efficiency and Landauer limit of photon-driven biological computation on planetary surfaces and of generalized computation in stellar energy capture structures (a.k.a. Dyson structures). It is suggested that CZs that involve nested structures or substellar objects could manifest unique observational signatures as cool far-infrared emitters. While these latter scenarios are entirely hypothetical, they offer a useful, complementary introduction to the potential universality of CZs.

Deep learning probability flows and entropy production rates in active matter.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework to estimate the score of this density. We show that the score, together with the microscopic equations of motion, gives access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles. To represent the score, we introduce a spatially local transformer network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of active particles undergoing motility-induced phase separation (MIPS). We show that a single network trained on a system of 4,096 particles at one packing fraction can generalize to other regions of the phase diagram, including to systems with as many as 32,768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Affinity-matured antibody with a disulfide bond in H-CDR3 loop.

Affinity maturation increases antigen-binding affinity and specificity of antibodies by somatic hypermutation. Various monoclonal antibodies against (4-hydroxy-3-nitrophenyl)acetyl (NP) were obtained during affinity maturation. Among them, highly matured anti-NP antibodies, such as E11 and E3, possess Cys96H and Cys100H in the complementarity-determining region 3 of the heavy chain, which would form a disulfide bond. In this study, we evaluated the effects of disulfide bonds on antigen binding by generating single-chain Fv (scFv) antibodies of E11 and its mutants, E11_C96KH/C100EH and E11_C96KH/C100QH, and determined their antigen-binding thermodynamics and kinetics. The binding affinities of the Cys mutants were lower than that of E11 scFv, indicating that the disulfide bond contributed to antigen binding, especially for stable complex formation. This was also supported by the decreased affinity of E11 scFv in the presence of a reducing agent. The crystal structures of NP-free and NP-bound E11 scFvs were determined at high resolution, showing the existence of a disulfide bond between Cys96H and Cys100H, and the antigen recognition mechanism, which could be compared with those of other anti-NP antibodies, such as germline-type N1G9 and matured-type C6, as reported previously. These structures could explain the molecular basis of changes in antigen-binding affinity and thermal stability in the absence or presence of antigens. Small-angle X-ray scattering further showed a local conformational change in E11 scFv upon antigen binding in solution.

Thermodynamic Stability Theories of Irreversible Processes and the Fourth Law of Thermodynamics.

Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs-Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested "fourth laws", this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation.

Ising Paradigm in Isobaric Ensembles.

We review recent work on Ising-like models with "compressible cells" of fluctuating volume that, as such, are naturally treated in NpT and µpT ensembles. Besides volumetric phenomena, local entropic effects crucially underlie the models. We focus on "compressible cell gases" (CCG), namely, lattice gases with fluctuating cell volumes, and "compressible cell liquids" (CCL) with singly occupied cells and fluctuating cell volumes. CCGs contemplate singular diameters and "Yang-Yang features" predicted by the "complete scaling" formulation of asymmetric fluid criticality, with a specific version incorporating "ice-like" hydrogen bonding further describing the "singularity-free scenario" for the low-temperature unusual thermodynamics of supercooled water. In turn, suitable CCL variants constitute adequate prototypes of water-like liquid-liquid criticality and the freezing transition of a system of hard spheres. On incorporating vacant cells to such two-state CCL variants, one obtains three-state, BEG-like models providing a satisfactory description of water's "second-critical-point scenario" and the whole phase behavior of a simple substance like argon. Future challenges comprise water's crystal-fluid phase behavior and metastable states.

Systems and Methods for Transformation and Degradation Analysis.

Modern concepts in irreversible thermodynamics are applied to system transformation and degradation analyses. Phenomenological entropy generation (PEG) theorem is combined with the Degradation-Entropy Generation (DEG) theorem for instantaneous multi-disciplinary, multi-scale, multi-component system characterization. A transformation-PEG theorem and space materialize with system and process defining elements and dimensions. The near-100% accurate, consistent results and features in recent publications demonstrating and applying the new TPEG methods to frictional wear, grease aging, electrochemical power system cycling-including lithium-ion battery thermal runaway-metal fatigue loading and pump flow are collated herein, demonstrating the practicality of the new and universal PEG theorem and the predictive power of models that combine and utilize both theorems. The methodology is useful for design, analysis, prognostics, diagnostics, maintenance and optimization.

Geometrothermodynamics of 3D Regular Black Holes.

We investigate a spherically symmetric exact solution of Einstein's gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions.

A Symmetric Form of the Clausius Statement of the Second Law of Thermodynamics.

Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals since. Thermodynamics still has unknown possibilities waiting to be explored. This paper begins with a brief review of Clausius's work on the second law of thermodynamics and a reassessment of the content of Clausius's statement. The review tells that what Clausius originally referred to as the second law of thermodynamics was, in fact, the theorem of equivalence of transformations (TET) in a reversible cycle. On this basis, a new symmetric form of Clausius's TET is proposed. This theorem says that the two transformations, i.e., the transformation of heat to work and the transformation of work from high pressure to low pressure, should be equivalent in a reversible work-to-heat cycle. New thermodynamic cyclic laws are developed on the basis of the cycle with two work reservoirs (two pressures), which enriches the fundamental of the second law of thermodynamics.