The article sets forth comprehensive basics of thermodynamics of chemical equilibrium as balance of the thermodynamic forces. Based on the linear equations of irreversible thermodynamics, De Donder definition of the thermodynamic force, and Le Chatelier's principle, new thermodynamics of chemical equilibrium offers an explicit account for multiple chemical interactions within the system. Basic relations between energetic characteristics of chemical transformations and reaction extents are based on the idea of chemical equilibrium as balance between internal and external thermodynamic forces, which is presented in the form of a logistic equation, containing only one new parameter. Solutions to the basic equation define the domain of states of the chemical system, from true equilibrium to true chaos. The new theory is derived exclusively from the currently recognized ideas and covers equilibrium thermodynamics as well as non-equilibrium thermodynamics in a unique concept.
A covariant formalism is used in order to examine the status of Maxwell equations and to unify the concept of balances, for all chemical engineering applications in relation with electrodynamics. The resulting formal structure serves as a discussion in studying the determinism of electromagnetic systems, and examining the theoretical foundations for a general classification of chemical engineering applications when non-conservative forces are concerned. A strategy for modeling such applications is then sketched and the balances for the main conserved and non-conserved extensive quantities are …
It is shown that that the exact solution of the Schrodinger equation for the molecule consisting of two atoms interacting via improved Tietz potential, the analytical expressions for the energy of the rotational-vibrational levels, partition function, free energy, mean energy and specific heat, obtained from the solution in the paper Exact analytical calculations of thermodynamic functions of gaseous substances", R. Khordad, A. Avazpour, and A. Ghanbari, Chemical Physics 517 (2019) 30, are incorrect.
In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exists. However this relation has been rigorously demonstrated only in a few cases in which one-way fluxes are well defined. In terms of its stochastic kinetic representation, we formulate the one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. For each kinetic cycle, the logarithm of the ratio of the steady-state forward …
All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a mean-field approach using activity coefficients. Thermodynamic consistency requires that rate equations do not obey to standard mass-action kinetics, but account for the interactions with concentration dependent kinetic constants. Many features of the ideal formulations are recovered. Crucially, the thermodynamic potential and the forces driving non-ideal chem…
We generalize thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macroscopic CRNs and mesoscopic CRNs plays an essential role in our results. The TUR shows that the product of the entropy production rate and the ratio of the scaled diffusion coefficient to the square of the rate of concentration change is bounded below by 2. The TSL states a trade-off relation between speed and thermodynamic quantities, the entropy production and the time…
We investigate the thermodynamic implications of two control mechanisms of open chemical reaction networks. The first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes. We show that the two mechanisms can be mapped one into the other and that the thermodynamic theories usually developed in the framework of concentration control can be applied to flux control as well. This implies that the thermodynamic potential and the fundamental forces driving chemical reaction networks out of equilibrium can be identified in th…
We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including non-ideal and open systems. For this purpose, we explicitly construct dual affine coordinate systems, which completely designate an information-geometric structure, using the extent of reactions and the affinities of reactions as coordinates on a linearly-constrained space of amounts of substances. The resulting structure induces a metric and a divergence (a function of two distributions of amounts), both expressed with chemical potentials. These quanti…
We develop a thermodynamic framework for closed and open chemical networks applicable to non-elementary reactions that do not need to obey mass action kinetics. It only requires the knowledge of the kinetics and of the standard chemical potentials, and makes use of the topological properties of the network (conservation laws and cycles). Our approach is proven to be exact if the network results from a bigger network of elementary reactions where the fast-evolving species have been coarse grained. Our work should be particularly relevant for energetic considerations in biosystems where the char…
We study a connection between chemical thermodynamics and information geometry. We clarify a relation between the Gibbs free energy of an ideal dilute solution and an information-geometric quantity called an $f$-divergence. From this relation, we derive information-geometric inequalities that give a speed limit for a changing rate of the Gibbs free energy and a general bound of chemical fluctuations. These information-geometric inequalities can be regarded as generalizations of the Cramér--Rao inequality for chemical reaction networks described by rate equations, where unnormalized concentrati…
The theory of chemical kinetics form the basis to describe the dynamics of chemical systems. Owing to physical and thermodynamic constraints, chemical reaction systems possess various structures, which can be utilized to characterize important physical properties of the systems. In this work, we reveal the Hessian geometry which underlies chemical reaction systems and demonstrate how it originates from the interplay of stoichiometric and thermodynamic constraints. Our derivation is based on kinetics, we assume the law of mass action and characterize the equilibrium states by the detailed balan…
Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction-diffusion systems to characterize chemical waves. Our main result is the definition of the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spe…
We consider growing open chemical reaction systems (CRSs), in which autocatalytic chemical reactions are encapsulated in a finite volume and its size can change in conjunction with the reactions. The thermodynamics of growing CRSs is indispensable for understanding biological cells and designing protocells by clarifying the physical conditions and costs for their growing states. In this work, we establish a thermodynamic theory of growing CRSs by extending the Hessian geometric structure of non-growing CRSs. The theory provides the environmental conditions to determine the fate of the growing …
The quasi-chemical organization of the potential distribution theorem -- molecular quasi-chemical theory (QCT) -- enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) As a way to regularize an ill-conditioned statistical thermodynamic problem; (b) As an introduction of and emphasis on the neighborship characteristics of a solute of interest; (c) Or as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly …
Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier $μ= \partial E/\partial N$ in the Euler-Lagrange variational equation for the ground state density as the chemical potential of the electrons. We first discuss why the Lagrange multiplier in this case is an arbitrary constant and therefore cannot be a physical characteristic of an atom or molecule. The switching of the energy derivative ("chemical potential") from $-I$ to $-A…
Chemical processes in closed systems are poorly controllable since they always relax to equilibrium. Living systems avoid this fate and give rise to a much richer diversity of phenomena by operating under nonequilibrium conditions. Recent experiments in dissipative self-assembly also demonstrated that by opening reaction vessels and steering certain concentrations, an ocean of opportunities for artificial synthesis and energy storage emerges. To navigate it, thermodynamic notions of energy, work and dissipation must be established for these open chemical systems. Here, we do so by building upo…
A Minimal Thermodynamically Consistent Chemical Oscillator
University of Luxembourg（卢森堡大学）；University of Strasbourg（斯特拉斯堡大学）；Heidelberg University（海德堡大学）；University of Trieste（的里雅斯特大学）；Northwestern University（西北大学）
We establish a Hessian geometric structure in chemical thermodynamics which describes chemical reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence and uniqueness condition of the equilibrium state is derived by using the Legendre duality inherent to the Hessian structure. The entropy production during a relaxation to the equilibrium state can be evaluated by the Bregman divergence. Furthermore, the equilibrium state is characterized by four distinct minimization problems of the divergence, which are o…
Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady state (NESS). In reality, these processes take place in finite systems containing a finite number of molecules. In such systems, a NESS can be reached with the help of an externally driven pump for which we introduce a simple model. Crucial parameters are the pumping rate and the finite size of the chemical reservoir. We apply this model to a simple biochemica…
Shanghai Jiao Tong University（上海交通大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Purdue University（普渡大学）
We introduce an explorative active learning (AL) algorithm based on Gaussian process regression and marginalized graph kernel (GPR-MGK) to explore chemical space with minimum cost. Using high-throughput molecular dynamics simulation to generate data and graph neural network (GNN) to predict, we constructed an active learning molecular simulation framework for thermodynamic property prediction. In specific, targeting 251,728 alkane molecules consisting of 4 to 19 carbon atoms and their liquid physical properties: densities, heat capacities, and vaporization enthalpies, we use the AL algorithm t…
We have established the detailed phase diagram of the prototypical deep eutectic solvent ethaline (ethylene glycol / choline chloride 2:1) as a function of the hydration level, in the bulk state and confined in the nanochannels of mesostructured porous silica matrices MCM-41 and SBA-15, with pore radii $R_P$ = 1.8 nm and 4.15 nm. For neat and moderately hydrated DESs, freezing was avoided and glassforming solutions were formed in all cases. For mass fraction of water above a threshold value $W_g'\approx30\%$, crystallization occurred and led to the formation of a maximally-freeze concentrated …
Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws
在这篇文章和一个配套文件中，我们概述了一个一般框架的热力学描述开放的化学反应网络，特别是关于代谢网络调节细胞生理和生化功能。我们首先介绍封闭网络“在一个盒子”，其热力学受到严格的物理约束：质量作用定律，过程的基本性，和细致平衡。我们进一步离题的溶剂的作用和网络独立性的自由能景观似乎未被承认的财产。然后，我们通过假设某些底物物质（恒化器）的浓度是固定的来打开系统，无论是因为通过与水库接触而被环境迅速调节，还是因为在时间窗口中几乎恒定。结果，系统被驱离平衡。内部物种网络中包含丰富的代数和拓扑结构：涌现的不可逆循环与非零亲和力相关，其对称性由守恒定律的破坏决定。这些中心的结果恢复之间的关系$a + b = s^Y$的基本亲和力$a$，打破守恒律$b$和恒化器的数量$s^Y$。我们分解的基本通量和亲和力在Schnakenberg的网络热力学理论的精神，为即将到来的治疗的线性制度，效率和紧耦合，自由能转导和热力学约束网络重建的稳态熵产生率。
