Thermodynamic Relations Research Articles

Fluctuation theorems in general relativistic stochastic thermodynamics

Fluctuation theorems in general relativistic stochastic thermodynamics

Speed limits and thermodynamic uncertainty relations for quantum systems with the non-Hermitian Hamiltonian

Speed limits and thermodynamic uncertainty relations for quantum systems with the non-Hermitian Hamiltonian

A non-isothermal phase-field crystal model with lattice expansion: analysis and benchmarks

Abstract We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The fundamental thermodynamic relation between internal energy and entropy, as well as entropy production, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within an entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.

Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology

Horizon thermodynamics and cosmological equations in standard cosmology provide a holographic-like connection between thermodynamic quantities on a cosmological horizon and in the bulk. It is expected that this connection can be modified as a holographic-like thermodynamic relation for dissipative and non-dissipative universes whose Hubble volume V varies with time t. To clarify such a modified thermodynamic relation, the present study applies a general formulation for cosmological equations in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe to the first law of thermodynamics, using the Bekenstein–Hawking entropy SBH and a dynamical Kodama–Hayward temperature TKH. For the general formulation, both an effective pressure pe of cosmological fluids for dissipative universes (e.g., bulk viscous cosmology) and an extra driving term fΛ(t) for non-dissipative universes (e.g., time-varying Λ(t) cosmology) are phenomenologically assumed. A modified thermodynamic relation is derived by applying the general formulation to the first law, which includes both pe and an additional time-derivative term f˙Λ(t), related to a non-zero term of the general continuity equation. When fΛ(t) is constant, the modified thermodynamic relation is equivalent to the formulation of the first law in standard cosmology. One side of this modified relation describes thermodynamic quantities in the bulk and can be divided into two time-derivative terms, namely ρ˙ and V˙ terms, where ρ is the mass density of cosmological fluids. Using the Gibbons–Hawking temperature TGH, the other side of this relation, TKHS˙BH, can be formulated as the sum of TGHS˙BH and [(TKH/TGH)-1]TGHS˙BH, which are equivalent to the ρ˙ and V˙ terms, respectively, with the magnitude of the V˙ term being proportional to the square of the ρ˙ term. In addition, the modified thermodynamic relation for constant fΛ(t) is examined by applying the equipartition law of energy on the horizon. This modified thermodynamic relation reduces to a kind of extended holographic-like connection when a constant TKH universe (whose Hubble volume varies with time) is considered. The evolution of thermodynamic quantities is also discussed, using a constant TKH model, extending a previous analysis (Komatsu in Phys Rev D 108:083515, 2023).

Covariant currents and a thermodynamic uncertainty relation on curved manifolds

A framework for defining stochastic currents associated with diffusion processes on curved Riemannian manifolds is presented. This is achieved by introducing an overdamped Stratonovich–Langevin equation that remains fully covariant under nonlinear transformations of state variables. This approach leads to a covariant extension of the short-time thermodynamic uncertainty relation, describing a trade-off between the total entropy production rate and thermodynamic precision associated with short-time currents in curved spaces and arbitrary coordinate systems.

Cross-diffusion waves by cellular automata modeling: Pattern formation in porous media.

Porous earth materials exhibit large-scale deformation patterns, such as deformation bands, which emerge from complex small-scale interactions. This paper introduces a cross-diffusion framework designed to capture these multiscale, multiphysics phenomena, inspired by the study of multi-species chemical systems. A microphysics-enriched continuum approach is developed to accurately predict the formation and evolution of these patterns. Utilizing a cellular automata algorithm for discretizing the porous network structure, the proposed framework achieves substantial computational efficiency in simulating the pattern formation process. This study focuses particularly on a dynamic regime termed "cross-diffusion wave," an instability in porous media where cross-diffusion plays a significant role-a phenomenon experimentally observed in materials like dry snow. The findings demonstrate that external thermodynamic forces can initiate pattern formation in cross-coupled dynamic systems, with the propagation speed of deformation bands primarily governed by cross-diffusion and a specific cross-reaction coefficient. Owing to the universality of thermodynamic force-flux relationships, this study sheds light on a generic framework for pattern formation in cross-coupled multi-constituent reactive systems.

Internal Energy, Fundamental Thermodynamic Relation, and Gibbs' Ensemble Theory as Emergent Laws of Statistical Counting.

Statistical counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent and identically distributed N sampling. Entropy provides the infinitesimal probability for an observed empirical frequency ν^ with respect to a probability prior p, when ν^≠p as N→∞. Following Callen's postulate and through Legendre-Fenchel transform, without help from mechanics, we show that an internal energy u emerges; it provides a linear representation of real-valued observables with full or partial information. Gibbs' fundamental thermodynamic relation and theory of ensembles follow mathematically. u is to ν^ what chemical potential μ is to particle number N in Gibbs' chemical thermodynamics, what β=T-1 is to internal energy U in classical thermodynamics, and what ω is to t in Fourier analysis.

Physicochemical properties of CF3OCF = CF2 in high-voltage switchgear: part 1. Decomposition characteristics and thermodynamic parameters

Abstract Recently, perfluoromethyl vinyl ether (CF3OCF = CF2) has been proposed to have the potential to replace SF6, but its arc-extinguishing ability is still unknown. To provide the necessary basic parameters for further study of arc extinguishing characteristics, this series of papers focuses on the physical and chemical properties of CF3OCF = CF2 arc plasma. The research content of this paper is decomposition characteristics and thermodynamic parameters. The geometric configuration, rotational inertia, and vibration frequency characteristics of CF3OCF = CF2 and its decomposition products were obtained at the B3LYP/6–311G(d,p) level. The energy of each particle was calculated at the CCSD(T)/cc-pVTZ level. The most likely decomposition path was CF3OCF = CF2→CF3+CF2CFO→CF2+CFO. The equilibrium compositions of arc plasma were calculated by the mass action law model. The main components of pure CF3OCF = CF2 after arc were C3F8, C3F6, C2F6, CF4, and CO. When CO2 was mixed in CF3OCF = CF2, with the increase of CO2 content, the main components after arc gradually became CF2O, CF4, CO2, and CO. The thermodynamic parameters such as density, specific enthalpy, and specific heat at constant pressure were obtained by thermodynamic relationship. Through ρC p and ρh, it can be inferred that the radial heat transfer capacity of CF3OCF = CF2 is not as good as SF6, but the energy dissipation capacity of axial heat convection is stronger than SF6, and the arc presents the characteristics of large radius and long length.

General relativistic stochastic thermodynamics

Based on the recent work [J. Stat. Phys. 190, 193 (2023), J. Stat. Phys. 190, 181 (2023)], we formulate the first law and the second law of stochastic thermodynamics in the framework of general relativity. These laws are established for a charged Brownian particle moving in a heat reservoir and subjecting to an external electromagnetic field in generic stationary spacetime background, and in order to maintain general covariance, they are presented respectively in terms of the divergences of the energy current and the entropy density current. The stability of the equilibrium state is also analyzed.

Universal thermodynamic relations with constant corrections for five-dimensional deSitter spacetime

Abstract Universal thermodynamic relations with constant corrections for five-dimensional de
Sitter spacetime

Thermal quasiparticle theory.

The widely used thermal Hartree-Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi-Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi-Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green's function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. A physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak's theorem.

Analysis and comparative study on the detonation performance of different heavy metal azides through theoretical calculations

Abstract In this paper, the detonation performance of different types of heavy metal azides is analyzed and compared using the detonation thermodynamic calculation method. Using the Virial-Peng-Long (VPL) equation of state (EOS) which based on the theoretical values of the 2-5th order virial coefficients of the Exponential-6 (Exp-6) potential to describe the high temperature and high pressure thermodynamic state of the gaseous detonation product N2, and the trinomial EOS Wu-Chen-Peng (WCP) which based on the universal Debye temperature specific volume function was used to describe the thermodynamic relations of the corresponding condensed metal product. Based on the VPL EOS and WCP EOS, the detonation velocity, detonation C-J (Chapmann-Jouguet) pressure and isentropic expansion P-V relations of detonation products for four kinds of metal azides: lead azide, silver azide, cuprous azide, and cupric azide, were obtained at different densities through detonation thermodynamic calculations. The detonation performance of different metal azides was compared and evaluated by combining detonation heat and gaseous product content. The reaults show that cupric azide has relatively better detonation velocity and work capacity, especially suitable for initiation by driving flyer. Lead azide and silver azide have higher detonation C-J pressure which are suitable to direct initiation.

Anomalous pressure-density relations and speed of sound in bubbly water systems.

The speed of sound in bubbly water is an important parameter in the wave equations governing pressure-density relations for turbulent multi-phase flow simulations. Recent molecular simulation results indicate that, for bubbles that are thermodynamically stable at finite volume conditions, the derivative of total pressure P with density ρ has a negative sign, complicating the interpretation of the speed of sound. We show that such a negative compressibility is thermodynamically consistent in a single-component two-phase model at finite volume, and identify an empirically derived equation of state to illustrate that this observation is not an artifact of small simulation length scales. To reconcile this thermodynamic relation with measurements of sound propagation, we decompose the derivative ∂P/∂ρ for bubbly water into its constituent phases to identify absorptive and transmissive contributors, both with an equation of state and using molecular simulations. We find that the speed of sound in the liquid phase remains real-valued while the bubble attenuates sound, giving a negative system compressibility. The inclusion of N2 molecules in molecular simulations illustrates that these observations are robust and hold also for mixtures. From these simulations, we also compute scattering functions for bubbly systems to identify oscillations associated with the speed of sound. Finally, the spherical harmonic modes of bubble oscillations are analyzed in the context of resonance with propagating waves.

Thermodynamic relation on higher-dimensional black hole with arbitrary cosmological constant

We investigated the Goon–Penco (GP) relation on higher-dimensional Reissner–Nordström black holes with an arbitrary cosmological constant. We found that the GP relation retained its form in four- and higher-dimensional spacetimes. Thus, the reactions in the black holes are universal with respect to dimensionality. Furthermore, the GP relation was found to be universal on any state of the black hole, including near-extremal and near-Nariai cases. Thus, it was shown that the GP relation was prevalent for higher-dimensional Reissner–Nordström black holes with an arbitrary cosmological constant regardless of the initial state.

Dissipation Bounds Precision of Current Response to Kinetic Perturbations.

The precision of currents in Markov networks is bounded by dissipation via the so-called thermodynamic uncertainty relation (TUR). In our Letter, we demonstrate a similar inequality that bounds the precision of the static current response to perturbations of kinetic barriers. Perturbations of such type, which affect only the system kinetics but not the thermodynamic forces, are highly important in biochemistry and nanoelectronics. We prove that our inequality cannot be derived from the standard TUR. Instead, it implies the standard TUR and provides an even tighter bound for dissipation. We also provide a procedure for obtaining the optimal response precision for a given model.

Empirical Determination of the Internal Energy, Enthalpy, Helmholtz Free Energy and Gibbs Free Energy of Polyethylene When One of the Thermodynamic Factors, Pressure, Volume, Temperature and Entropy, is Constant

In a previous report the internal energy, U, enthalpy, H, Helmholtz free energy, A, and Gibbs free energy, G, of polyethylene (PE) were determined when two of the thermodynamic factors X or Y were constant, where X and Y were two of the four factors, pressure, P, volume, V, temperature, T, and entropy, S. In this work these various energies were evaluated when one of the four thermodynamic factors is constant based on the thermodynamic conditions. In the case of the isothermal process with T = const, the internal energy was expressed by U T, enthalpy by H T, Helmholtz free energy by A T and Gibbs free energy by G T. The heat, TS T , and the work, PTV T, in the isothermal process were evaluated based on the thermodynamic relation that H T − G T = TS T and H T − U T = P T V T . In the isothermal process the changes of PTV T were large and dominant compared to those of TS T when V T, S T and P T increased independently under constant T, while the changes of TS T were small and almost constant at constant T. The isobaric process with P = const was characterized by the changes of TPS P being large and dominant compared to those of PV P when V P, S P and T P increased independently under constant P, while the isoentropic process with S = const was characterized by the changes of PSV S being large and dominant compared to those of TSS when T S, P S and V S increased independently under constant S where the subscripts, T, P, S, mean the isothermal, isobaric and isoentropic ensembles, respectively.

Exact time-dependent thermodynamic relations for a Brownian particle moving in a ratchet potential coupled with quadratically decreasing temperature.

The thermodynamic relations for a Brownian particle moving in a discrete ratchet potential coupled with quadratically decreasing temperature are explored as a function of time. We show that this thermal arrangement leads to a higher velocity (lower efficiency) compared to a Brownian particle operating between hot and cold baths, and a heat bath where the temperature linearly decreases along with the reaction coordinate. The results obtained in this study indicate that if the goal is to design a fast-moving motor, the quadratic thermal arrangement is more advantageous than the other two thermal arrangements. In contrast, the entropy, entropy production rate, and entropy extraction rate are significantly larger in the case of a quadratically decreasing temperature compared to the linearly decreasing temperature case and piecewise constant temperature case. Furthermore, the thermodynamic features of a system consisting of several Brownian ratchets arranged in a complex network are explored. The theoretical findings exhibit that as the network size increases, the entropy, entropy production, and entropy extraction of the system also increase, showing that these thermodynamic quantities exhibit extensive property. As a result, as the number of lattice sizes increases, thermodynamic relations such as entropy, entropy production, and entropy extraction also step up, confirming that these complex networks cannot be reduced to a corresponding one-dimensional lattice. However, in the long time limit, thermodynamic relations such as velocity, entropy production rate, and entropy extraction rate become independent of the network size. These results are also confirmed via a continuum Fokker-Planck model for the overdamped case.

Unified hierarchical relationship between thermodynamic tradeoff relations.

Recent years have witnessed a surge of discoveries in the studies of thermodynamic inequalities: the thermodynamic uncertainty relation (TUR) and the entropic bound (EB) provide a lower bound on the entropy production (EP) in terms of nonequilibrium currents; the classical speed limit (CSL) expresses the lower bound on the EP using the geometry of probability distributions; the power-efficiency (PE) tradeoff dictates the maximum power achievable for a heat engine given the level of its thermal efficiency. In this study, we show that there exists a unified hierarchical structure encompassing all of these bounds, with the fundamental inequality given by an extension of the TUR (XTUR) that incorporates the most general range of currentlike and state-dependent observables. By selecting more specific observables, the TUR and the EB follow from the XTUR, and the CSL and the PE tradeoff follow from the EB. Our derivations cover both Langevin and Markov jump systems, with the first proof of the EB for the Markov jump systems and a more generalized form of the CSL. We also present concrete examples of the EB for the Markov jump systems and the generalized CSL.

Numerical simulation of phase transition with the hyperbolic Godunov-Peshkov-Romenski model

In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.

A Hollow Hemispherical Mixed Matrix Lithium Adsorbent with High Interfacial Interaction for Lithium Recovery from Brine

Mixed matrix lithium adsorbents have attracted much interest for lithium recovery from brine. However, the absence of an interfacial interaction between the inorganic lithium-ion sieves (LISs) and the organic polymer matrix resulted in the poor structural stability and attenuated lithium adsorption efficiency. Here, a novel hollow hemispherical mixed matrix lithium adsorbent (H-LIS) with high interfacial compatibility was constructed based on mussel-bioinspired surface chemistry using a solvent evaporation induced phase transition method. The effects of types of functional modifiers, LIS loading amount, adsorption temperature and pH on their structural stability and lithium adsorption performance were systematically investigated. The optimized H-LIS adsorbent with the LIS loading amount of 50 wt.% possessed the structural merit that the LIS functionally modified by dopamine exposed on both the inner and outer surfaces of the hollow hemispheres. At the best adsorption pH of 12.0, it showed a comparable lithium adsorption capacity of 25.68 mg·g−1 to the powdery LIS within 4 h, favorable adsorption selectivity of Mg/Li and good reusability that could maintain over 90% of lithium adsorption capacity after the LiCl adsorption—0.25 M HCl pickling-DI water cleaning cycling processes for three times. The interfacial interaction mechanism of H-LIS for lithium adsorption was innovatively explored via advanced microcalorimetry technology. It suggested the nature of the Li+ adsorption process was exothermic and dopamine modification could reduce the activation energy for lithium adsorption from 15.68 kJ·mol−1 to 13.83 kJ·mol−1 and trigger a faster response to Li+ by strengthening the Li+-H+ exchange rate, which established the thermodynamic relationship between the structure and Li+ adsorption performance of H-LIS. This work will provide a technical support for the structural regulation of functional materials for lithium extraction from brine.