Duhem Relation Research Articles

The development of thermodynamically consistent and physics-informed equation-of-state model through machine learning

Ab initio molecular dynamics (AIMD) simulations have become an important tool used in the construction of equations of state (EOS) tables for warm dense matter. Due to computational costs, only a limited number of system state conditions can be simulated, and the remaining EOS surface must be interpolated for use in radiation-hydrodynamic simulations of experiments. In this work, we develop a thermodynamically consistent EOS model that utilizes a physics-informed machine learning approach to implicitly learn the underlying Helmholtz free-energy from AIMD generated energies and pressures. The model, referred to as PIML-EOS, was trained and tested on warm dense polystyrene producing a fit within a 1% relative error for both energy and pressure and is shown to satisfy both the Maxwell and Gibbs–Duhem relations. In addition, we provide a path toward obtaining thermodynamic quantities, such as the total entropy and chemical potential (containing both ionic and electronic contributions), which are not available from current AIMD simulations.

Analog of the Sommerfeld Law in Quantum Vacuum

The activation temperature T in the de Sitter environment is twice the Gibbons–Hawking temperature, related to the cosmological horizon. We consider the activation temperature as the local temperature of the de Sitter vacuum, and construct the local thermodynamics of the de Sitter state. This thermodynamics includes also the gravitational coupling K and the scalar Riemann curvature mathcal{R} as the thermodynamically conjugate variables. These variables modify the thermodynamics of the Gibbs–Duhem relation in the de Sitter state. The free energy density is proportional to - {{T}^{2}}, which is similar to that in the nonrelativistic Fermi liquids and in relativistic matter with equation of state w = 1. The local entropy is proportional to the local temperature, while the total entropy inside the cosmological horizon is A{text{/}}4G, where A is the area of the horizon. This entropy is usually interpreted as the entropy of the cosmological horizon. We also consider the possible application of the de Sitter thermodynamics to the Schwarzschild–de Sitter black hole and to black and white holes with the de Sitter cores.

Study of phase equilibria and thermodynamic properties of liquid mixtures using the integral equation theory: Application to water and alcohol mixtures.

A theoretical method for calculating the thermodynamic properties and phase equilibria of liquid-liquid mixtures using the integral equation theory is proposed. The solvation chemical potentials of the two components are evaluated by the integral equation theory and the isothermal-isobaric variation of the total density with composition is determined to satisfy the Gibbs-Duhem relation. Given the density of a pure component, the method can calculate the densities of the mixture at any composition. Furthermore, it can treat the phase equilibrium without thermodynamic inconsistency with respect to the Gibbs-Duhem relation. This method was combined with the reference interaction-site model integral equation theory and applied to mixtures of water + 1-alcohol by changing the alcohol from methanol to 1-butanol. The destabilization of the mixing Gibbs energy by increasing the hydrophobicity of the alcohol and demixing of the water-butanol mixture were reproduced. However, quantitative agreement with experiments is not satisfactory, and further improvements of the integral equation theory and the molecular models are required.

Exponential corrected thermodynamics of black holes

It has been reported that the black hole entropy is modified by an exponential term due to the non-perturbative corrections interpreted as quantum effects. We now find the impact of such modification on the black hole mass and other thermodynamics quantities. We find that the Schwarzschild black hole mass decreased by quantum corrections. Hence, we study exponential corrected thermodynamics and statistics of black holes by computing the partition function. We obtain the particular condition on the event horizon radius to satisfy the Smarr–Gibbs–Duhem relation in the presence of quantum correction. As we know, the Schwarzschild black hole is unstable, while the effect of exponential correction is the stability of 4D Schwarzschild black hole as well as the Schwarzschild-AdS black hole at a small area. On the other hand, a 5D Schwarzschild black hole is completely unstable. The effect of the quantum correction on the Reissner–Nordström black hole is the black thermodynamics instability at quantum scales. Finally, we consider the most general case of charged AdS black hole and study the corrected thermodynamics.

Influence of Proton Activity Gaps between Electrodes on Open-Circuit Potential of H2/H2 and H2/Air Cells

Polymer -electrolyte-fuel-cell open-circuit voltages (OCVs) are exactly defined by equation (1), where cathode and anode proton activities [(aH+)cathode and (aH+)anode, respectively] usually are identical, so the third term in the right-hand side of equation (2) is ignored.OCV=E0+RT/2F*ln(a1/2 O2*(a2 H+)cathode/aH2O)-RT/2F*ln((a2 H+)anode/aH2) (1)=E0+RT/2F*ln(a1/2 O2*aH2/aH2O)+RT/2F*ln((a2 H+)cathode/(a2 H+)anode) (2)Water vapor pressure is a colligative property that fundamentally correlates to electrolyte concentrations in aqueous solutions. Proton activity is a function of acid concentration, such as pH, when electrolytes are acids. In polymer-electrolyte membranes, water vapor pressure and acid concentration are understood as relative humidity (RH) and water uptake (λ), respectively, where λ represents number of water molecules per sulfonic acid molecule. Several investigations have reported the relationship between RH and λ, meaning that proton activities and associated water uptakes are intimately related to RH.In actual fuel cell operation, cathode RH is determined by ambient-atmosphere and/or humidifier RH(s), and anode RH depends on hydrogen-circulator RH. Therefore, RH is not always identical at both electrodes, and the difference between electrode RHs is considerable during dry operation of polymer electrolyte fuel cells. Therefore, the third term in the right-hand side of equation (2) may be significant for dry operation.We measured OCVs when hydrogen was supplied to both electrodes at 80°C. One electrode (A) was fixed at 30% RH, while RH at the other electrode (B) was varied (0, 5, 10, 20, and 30%). Measured OCVs varied from 0 to 75 mV. For fuel cell tests, electrode A was supplied with hydrogen at 30% RH; electrode B, oxygen at 0, 5, 10, 20, and 30% RH. OCVs deviated from that measured when RH at electrode B was 30%, increasing from 0 to 60 mV with decreasing RH at electrode B. Results are also shown in Figure 1.Proton activities of both electrodes were thermodynamically calculated. The Gibbs–Duhem relation was applied to obtain molar Gibbs free energies of water and sulfonic acid, and proton activity coefficient was calculated using the Gibbs free energy of sulfonic acid and the relationship between RH and λ1–4, assuming that protons and sulfonic anions show identical ionic-activity coefficients. OCVs were estimated using the third term in the right-hand side of equation (2). Results are shown in Figure 1.Fuel-cell current–voltage performance was poor when RHs at the anode and cathode were 30 and 20%, respectively. To determine kinetic current, we measured the oxygen-reduction reaction (ORR) using a rotating-disk electrode (RDE) in concentrated-acid aqueous solutions, which modeled catalyst-layer ionomers. Kinetic currents decreased with acid concentrations.References T. A. Zawodzinski, Jr., C. Derouin, S. Radzinski, R. J. Sherman, V. T. Smith, T. E. Springer and S. Gottesfeld , J. Electrochem. Soc., 140,1041 (1993)P. K. Das and A. Z. Weber, Proceedings of the ASME 2013 11th Fuel Cell Science, Engineering and Technology Conference, Fuel Cell 18010 (2013)V. A. Sethuraman, J. W. Weidner, A. T. Haug, S. Motupally,b and L. V. Protsailo, J. Electrochem. Soc., 155, B50 (2008)A. Kusoglu and A. Z. Weber, Chem. Rev., 117, 987 (2017) Figure 1

The Uniqueness of a Correction to Interaction Parameter Formalism in a Thermodynamically Consistent Manner

Polynomial representation of partial excess Gibbs energy (i.e., activity coefficient) in multicomponent dilute solution has been widely used after Wagner. Although Wagner’s Interaction Parameter Formalism has been known to be only strictly valid at infinite dilute concentration, it has been used often, even at finite concentration, due to its mathematical simplicity. Nevertheless, several attempts have been made to correct the formalism to be thermodynamically consistent at finite concentration. Among those, Unified Interaction Parameter Formalism proposed by Pelton and Bale, which may be considered as an extension of Darken’s quadratic formalism, has obtained much attention. However, there have been much confusion and debate about the way of the correction. Recently, a thermodynamic analysis was reported that there are infinite numbers of ways to correct Wagner’s formalism to be thermodynamically consistent, which may prevent one from using the Unified Interaction Parameter Formalism with confidence. In the present article, the correction to the Wagner’s formalism is discussed by revisiting Darken’s condition of the thermodynamic consistency. It is shown that the correction to the Wagner’s formalism can be made uniquely. It is pointed out that to ensure the thermodynamic consistency among the activity coefficients of all components, Gibbs–Duhem relation and Maxwell relation among all components including solvent–solute, must be obeyed. Derived expressions for activity coefficients of all components by path-independent integration are also shown to be the same as those obtained by differentiating a corresponding integral excess partial Gibbs energy.

Distribution of electropotential in the electrode area of a solid state ion electrolyte

A solid state electrolyte is considered as a system consisting of cations moving through the volume of a solid body and anions whose mobility can be neglected due to their large size compared to the size of the cations. Accordingly, in the homogeneous case local charge compensation takes place. Under the action of an external electric field, cations create in the near electrode area inhomogeneous redistribution of mobile charges and electric field. The model is used for the statistical­mechanical description of high­temperature ionic conductors and current sources. To obtain the free energy functional of the mobile charge subsystem depending on the distribution of their density, the cluster expansion scheme for the renormalized Mayer functions is used. The Hamiltonian of a system consisting of electric charges moving in the field of single­particle cell potentials of average forces is used as the basis one. The binary function of the host system is expressed in terms of the screened potentials and the potentials of the average forces based on the results of the method of collective variables. The internal energy of the system is calculated taking into account the short­ and long­range effects. The Gibbs – Duhem relation was used for calculating the free energy functional of the system. The distribution of the number density of moving particles and the electric potential in the near electrode region were found from the condition of extremality of the free energy. The potentials of average forces are obtained as a result of solving a system of integral equations in the lattice approximation, with accounting of the short­ and long­range effects. The transition from the correlative function to the correlation function allowed us to identify the correlated and uncorrelated parts of the electric potential. The linear contributions of the deviation of the charge concentrations from a uniform distribution to the chemical potential are considered. The calculations take into account the contribution of the correlation between the particles in the first three coordination spheres that leads to attraction of the first, repulsion of the second and third neighbors. The description is carried out using a linear differential equation of the fourth­order with complex values of the roots of the characteristic equation. The paper analyzes the results of the analytical solution.

Entropy production by thermodynamic currents in ambipolar conductors with identical spin dynamics characteristics between holes and electrons

We have evaluated the role of spin current in the energy dissipation mechanism in ambipolar conductors with identical spin-related characteristics between holes and electrons. Application of the Gibbs–Duhem relation to ambipolar conductors establishes a thermodynamic relation between the spin-dependent chemical potentials of holes and electrons, inducing an asymmetric spin splitting between the hole and electron chemical potentials. This yields two types of spin relaxation so as to allow the antiparallel spin current, where hole and electron spins flow in the opposite direction, to have a large spin diffusion length, but to retain that of the parallel spin current at a standard value.

Simulating Osmotic Equilibria: A New Tool for Calculating Activity Coefficients in Concentrated Aqueous Salt Solutions.

Herein, a new theoretical method is presented for predicting osmotic equilibria and activities, where a bulk liquid and its corresponding vapor phase are simulated by means of molecular dynamics using explicit polarization. Calculated time-averaged number density profiles provide the amount of evaporated molecules present in the vapor phase and consequently the vapor-phase density. The activity of the solvent and the corresponding osmotic coefficient are determined by the vapor density at different solute concentrations with respect to the reference vapor density of the pure solvent. With the extended Debye-Hückel equation for the activity coefficient along with the corresponding Gibbs-Duhem relation, the activity coefficients of the solutes are calculated by fitting the osmotic coefficients. A simple model based on the combination of Poisson processes and Maxwell-Boltzmann velocity distributions is introduced to interpret statistical phenomena observed during the simulations, which are related to evaporation and recondensation. This method is applied to aqueous dysprosium nitrate [Dy(NO3)3] solutions at different concentrations. The obtained densities of the liquid bulk and the osmotic and activity coefficients are in good agreement with the experimental results for concentrated and saturated solutions. Density profiles of the liquid-vapor interface at different concentrations provide detailed insight into the spatial distributions of all compounds.

Thermodynamics of gravitational clustering phenomena: N-body self-gravitating gas on the sphere

This work is devoted to the thermodynamics of gravitational clustering, a collective phenomenon with a great relevance in the N-body cosmological problem. We study a classical self-gravitating gas of identical non-relativistic particles defined on the sphere by considering gravitational interaction that corresponds to this geometric space. The analysis is performed within microcanonical description of an isolated Hamiltonian system by combining continuum approximation and the steepest descend method. According to numerical solution of resulting equations, the gravitational clustering can be associated with two microcanonical phase transitions. A first phase transition with a continuous character is associated with breakdown of SO(4) symmetry of this model. The second one is the gravitational collapse, whose continuous or discontinuous character crucially depends on the regularization of short-range divergence of gravitation potential. We also derive the thermodynamic limit of this model system, the astrophysical counterpart of the Gibbs–Duhem relation, the order parameters that characterize its phase transitions and the equation of state. Other interesting behavior is the existence of states with negative heat capacities, which appear when the effects of gravitation turn dominant for energies sufficiently low. Finally, we comment on the relevance of some of these results in the study of astrophysical and cosmological situations. Special interest deserves the gravitational modification of the equation of state due to the local inhomogeneities of matter distribution. Although this feature is systematically neglected in studies about universe expansion, the same one is able to mimic an effect that is attributed to the dark energy: a negative pressure.

Thermodynamic aspects of capillarity and electrocapillarity of solid interfaces

In the previous paper (Gutman, JOSSEC 18:3217–3237, 2014), we have shown that the main problem in capillarity and electrocapillarity of solid surfaces is the lack of clarity in determining the surface stress and basic equations. Now, we continue the survey of efforts to solve this problem and show origins of erroneous results, accenting some important items: comparative analysis of Gibbs and Guggenheim approaches in surface thermodynamics (a geometrical dividing surface and finite-thickness surface layer, respectively), transformation of fundamental equations on per-unit-area basis to obtain Gibbs adsorption equation for finite-thickness surface layer, different attempts to derive the thermodynamic definition of “surface stress” in frames of Gibbs’ theory (including Shuttleworth’s approach), atomistic calculations of surface stress, surface stress in rational continuum mechanics, “modifications” of Gibbs–Duhem relations made for solid interface, and Maxwell relations in capillarity and electrocapillarity of solid interface. It is shown that the erroneous Shuttleworth’s approach is present in an explicit or implicit form in all efforts to introduce the surface stress in frames of Gibbsian theory (although Gibbs did not introduce surface stress). Therefore, “modernizations” or “generalizations” of the Gibbs–Duhem relation, the Gibbs adsorption equation, and the Lippmann equation to adopt them for a solid surface are unnatural and not necessary. Therefore, we recommend withdrawing the Shuttleworth equation and its consequences from circulation, including the IUPAC Recommendations.

Remarks about the thermodynamics of astrophysical systems in mutual interaction and related notions

.Aspects concerning the thermodynamics of astrophysical systems are discussed, generally, and also more specifically those relating to astrophysical systems in mutual interaction (or the so-called open astrophysical systems). A special interest is devoted in this paper to clarifying several misconceptions that are still common in the recent literature, such as the direct application to the astrophysical scenario of notions and theoretical frameworks that were originally conceived to deal with extensive systems of everyday practice (large systems with short-range interactions). This discussion starts by reviewing the current understanding of the notion of negative heat capacity. Beyond this, to clarify its physical relevance, the conciliation of this notion with classical fluctuation theory is discussed, as well as equilibrium conditions concerning systems with negative heat capacities. These results prompt a revision of our understanding about critical phenomena, phase transitions and the so-called zeroth law of thermodynamics. Afterwards, general features about the thermodynamics of astrophysical systems are presented through the consideration of simple models available in the literature. Particular attention is devoted to the influence of evaporation on the macroscopic behavior of these systems. These antecedents are then applied to a critical approach towards the thermodynamics of astrophysical systems in mutual interaction. It is discussed that the long-range character of gravitation leads to the incidence of long-range correlations. This peculiarity imposes a series of important consequences, such as the non-separability of a single astrophysical structure into independent subsystems, the breakdown of additivity and conventional thermodynamic limit, a great sensibility of the macroscopic behavior to the external conditions, the restricted applicability of the so-called thermal contact in astrophysics, and hence, the non-relevance of conventional statistical ensembles in this scenario. To clarify how some of conventional notions and theoretical frameworks could be extended to open astrophysical systems, an exploratory study of a paradigmatic situation is presented: a binary astrophysical system. This analysis is carried out in the framework of the quadrupole approximation, which represents the lowest coupling among internal and collective degrees of freedom. Apparently, collective motions are responsible for a non-linear energy interchange among the astrophysical systems. This mechanism introduces some modifications in stationary and stability conditions for the thermodynamic equilibrium such as a generalization of Thirring’s stability condition for systems with negative heat capacities (1970 Z. Phys. 235 339). Additionally, the stability of collective motions of this binary astrophysical system is also discussed, which is related to the low energy thermodynamic behavior of the model discussed by Votyakov and colleagues (2002 Phys. Rev. Lett. 89 031101). The thermodynamic limit for self-gravitating gas of identical non-relativistic point particles is then derived and compared with other different proposals. The astrophysical counterpart of the Gibbs–Duhem relation is obtained and compared with the recent proposal of Latella and colleagues (2015 Phys. Rev. Lett. 114 230601). Finally, the incidence of non-extensivity during the merger of two identical astrophysical systems is analyzed. Contrary to the situation considered in the Gibbs paradox, the merger is an irreversible process that crucially depends on the existence (or non-existence) of the external gravitational influence of other systems.

Equation oriented mixed micellization modeling based on asymmetric Margules-type formulations

The determination of the composition of mixed micellar systems is a major problem since only the composition of the total micellar solution is accessible to the experimenter. A new approach is introduced in the present work based on Equation Oriented Optimization and Margules asymmetric formulations which is not restricted to the number of components and guarantees the applicability of the Gibbs–Duhem relation. The method is validated through its application to systems from literature and the quality of the solutions is tested with already published data and by comparison with other approaches. We do also show how excess properties can be predicted and that the excess entropy is not zero as assumed by the original regular and sub-regular solution theories.

Area product and mass formula for Kerr–Newman–Taub–NUT spacetime

We derive area product, entropy product, area sum and entropy sum of the event horizon and Cauchy horizons for Kerr–Newman–Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. We observe that these thermodynamic products are not universal (mass-independence) for this black hole (BH), whereas for Kerr–Newman (KN) BH such products are universal (mass-independence). We also examine the entropy sum and area sum. It is shown that they all depend on mass, charge and NUT parameter of the background spacetime. Thus, we can conclude that the universal (mass-independence) behavior of area product and entropy product, area sum and entropy sum for Kerr–Newman–Taub–NUT (KNTN) BH fails and which is also quite different from KN BH. We further show that the KNTN BH do not possess first law of BH thermodynamics and Smarr–Gibbs–Duhem relations, and that such relations are unlikely in the KN case. The failure of these aforementioned features are due to presence of the nontrivial NUT charge which makes the spacetime to be asymptotically non-flat, in contrast with KN BH. The other reason of the failure is that Lorentzian KNTN geometry contains Dirac–Misner type singularity, which is a manifestation of a nontrivial topological twist of the manifold. The BH mass formula and Christodoulou–Ruffini mass formula for KNTN BHs are also derived. Finally, we compute the area bound which is just Penrose like inequality for event horizon. From area bound we derive entropy bound. These thermodynamic products on the multi-horizon play a crucial role in BH thermodynamics to understand the microscopic nature of BH entropy.

Investigations of the Chemical Potentials of Dissolved Water and H2S in CO2 Streams Using Molecular Dynamics Simulations and the Gibbs–Duhem Relation

Water that accompanies CO2 during its pipeline transport presents a hazard due to rust and clathrate formation. Rusty pipeline walls favors adsorption of water and other impurities as an additional aqueous phase over condensing out as liquid droplets. The Gibbs phase rule prohibits the system from reaching full equilibrium since the continuous flow provides an ongoing supply of all phases. We present a scheme for free energy minimization under constraints of mass and heat transport that can predict the phase distribution and corresponding compositions. Molecular dynamics simulations and the Gibbs–Duhem relation are used to derive consistent infinite dilution chemical potentials for CO2 and H2S dissolved in water and H2O and H2S dissolved in CO2. Simplified activity coefficient expressions are derived and applied to analysis of hydrate risk formation. Applications of our approach are illustrated by estimating the tolerable water concentration in CO2 before water forms hydrate directly or adsorbs onto the r...

Non-applicability of the Gibbs-Duhem relation in nonextensive thermodynamics. Case of micellar solutions.

This work is a discussion on the applicability of the Gibbs-Duhem relationship. We show that it does not exist in the nonextensive thermodynamic approaches. To illustrate this, we have chosen to present the properties of three surfactants (dodecyltrimethylammonium bromide (DTABr), sodium dodecyl sulfate (SDS), sodium decanoate (NaDec) in aqueous solutions at 298 K) whose behavior after the micellization threshold can be described by the rules of the nonextensive thermodynamics. We show that the Gibbs-Duhem relationship does not apply to these systems and we propose to formalize the deviation from this law. The consequences of this study are discussed for the different approaches that involve the use of Gibbs-Duhem relation in the case of micellized solutions. In particular, the applicability of the Gibbs relation which links surface tension and the chemical potentials of solutes is considered. More generally, this study warns against the blind application of the Gibbs-Duhem (or Gibbs) relation, to any system.

Theoretical problems in solid electrocapillarity

The main problem in electrocapillarity of solid electrodes is the lack of clarity in determining the surface stress and basic equations. Within the framework of the Gibbs concept of geometrical dividing surface, the “surface stress” cannot be defined because methods of continuum mechanics can be applied to a physical surface layer (of finite thickness), but not to a mathematical surface. Gibbs never used the concept of surface stress, introducing only “surface tension” for a liquid electrode and “closely related quantity” for a solid electrode. Revisiting the derivation of the Gibbs adsorption equation, we prove its applicability to solid surfaces without the limiting requirement of constant state of strain, which was undeservedly interpreted by Eriksson as a shortcoming of the Gibbs theory caused to look for other approaches to surface stress problem. A critical analysis shows that the attempts (Shuttleworth, Eriksson, Couchman, Gokhstein, Weissmuller, etc.) to create a thermodynamic definition of the surface stress (as well as the formulation of fundamental thermodynamic equations and Maxwell relations operating with surface stresses) contain mathematical defects. It is shown that confusing interpretations of some Gibbs’ concepts encountered in the literature have led to “modifications” of the Lippmann equation based on the critical error in the Gibbs–Duhem relation due to the occurrence of an extensive variable, which is inadmissible. The famous Lippmann equation should not be modified, and it remains a unique electrocapillary relation applicable to liquid and solid electrodes.

Geometrothermodynamics: comments, criticisms, and support

We write explicitly the Euler identity and the Gibbs–Duhem relation for thermodynamic potentials that are not homogeneous first-order functions of their natural extensive variables. We apply the rules to the theory of geometrothermodynamics and show how the use of the natural extensive variables, instead of the modified ones, leads to misleading results. We further reveal some other ambiguities and inconsistencies in the theory and we make new suggestions.

Volume term of work of critical nucleus formation in terms of chemical potential difference relative to equilibrium one

The work of formation of a critical nucleus is sometimes written as W=nΔμ+γA. The first term Wvol=nΔμ is called the volume term and the second term γA the surface term with γ being the interfacial tension and A the area of the nucleus. Nishioka and Kusaka [J. Chem. Phys. 96 (1992) 5370] derived Wvol=nΔμ with n=Vβ/vβ and Δμ=μβ(T,pα)−μα(T,pα) by rewriting Wvol=−(pβ−pα)Vβ by integrating the isothermal Gibbs–Duhem relation for an incompressible β phase, where α and β represent the parent and nucleating phases, Vβ is the volume of the nucleus, vβ, which is constant, the molecular volume of the β phase, μ, T, and p denote the chemical potential, the temperature, and the pressure, respectively. We note here that Δμ=μβ(T,pα)−μα(T,pα) is, in general, not a directly measurable quantity. In this paper, we have rewritten Wvol=−(pβ−pα)Vβ in terms of μre−μeq, where μre and μeq are the chemical potential of the reservoir (equaling that of the real system, common to the α and β phases) and that at equilibrium. Here, the quantity μre−μeq is the directly measurable supersaturation. The obtained form is similar to but slightly different from Wvol=nΔμ.

An activity model for phase equilibria in the H2O–CO2–NaCl system

We present a semi-empirical thermodynamic model with uncertainties that encompasses the full range of compositions in H2O–CO2–NaCl mixtures in the range of 10–380°C and 1–3500bars. For binary H2O–CO2 mixtures, the activity–composition model is built from solubility experiments. The parameters describing interactions between H2O and CO2 are independent of the absolute thermodynamic properties of the end-members and vary strongly non-linearly with pressure and temperature. The activity of water remains higher than 0.88 in CO2-saturated solutions across the entire pressure–temperature range. In the H2O–NaCl system, it is shown that the speciation of aqueous components can be accounted for by a thermodynamic formalism where activities are described by interaction parameters varying with intensive properties such as pressure and temperature but not with concentration or ionic strength, ensuring consistency with the Gibbs–Duhem relation. The thermodynamic model reproduces solubility experiments of halite up to 650°C and 10kbar, and accounts for ion pairing of aqueous sodium and chloride ions with the use of associated and dissociated aqueous sodium chloride end-members whose relative proportions vary with salinity. In the H2O–CO2–NaCl system, an activity–composition model reproduces the salting-out effect with interactions parameters between aqueous CO2 and the aqueous species created by halite dissolution. The proposed thermodynamic properties are compatible with the THERMOCALC database (Holland and Powell, 2011) and the equations used to retrieve the activity model in H2O–CO2 can be readily applied to other systems, including minerals.