Conservation-Dissipation Formalism for Soft Matter Physics: II. Application to Non-isothermal Nematic Liquid Crystals

To most existing non-equilibrium theories, the modeling of non-isothermal processes was a hard task. Intrinsic difficulties involved the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrated that thermodynamically consistent models in either vectorial or tensorial forms could be constructed within the framework of Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model were shown to be special cases of our new vectorial and tensorial models in the isothermal, incompressible and stationary limit. Most importantly, from above examples, it was learnt that mathematical modeling based on CDF could easily solve the issues relating with non-isothermal situations in a systematic way. The first and second laws of thermodynamics were satisfied simultaneously. The non-equilibrium temperature was defined self-consistently through the partial derivative of entropy function. Relaxation-type constitutive relations were constructed, which gave rise to the classical linear constitutive relations, like Newton's law and Fourier's law, in stationary limits. Therefore, CDF was expected to have a broad scope of applications in soft matter physics, especially under the complicated situations, such as non-isothermal, compressible and nanoscale systems.Comment: 29 page

Thermodynamics for Reduced Models of Chemical Reactions by PEA and QSSA

Partial equilibrium approximation (PEA) and quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies mainly focus on the accuracy of solutions before and after applying model reduction. While, in this paper we start from a thermodynamic view, and try to establish a quantitative connection on the essential thermodynamic quantities, like entropy production rate, free energy dissipation rate and entropy flow rate, between the original reversible chemical mass-action equations and the reduced models by either PEA or QSSA. Our results reveal that the PEA and QSSA do not necessarily preserve the nice thermodynamic structure of the original full model during the reduction procedure (e.g. the loss of non-negativity of free energy dissipation rate), especially when adopting the algebraic relations in replace of differential equations. These results are further validated though the application to Michaelis-Menten reactions analytically and numerically as a prototype. We expect our study would motivate a re-examination on the effectiveness of various model reduction or approximation methods from a new perspective of non-equilibrium thermodynamics.Comment: 30 pages, 2 figures, 1 tabl

To what extent can control policies influence the epidemic spreading? -- A data-driven analysis based on the first wave of COVID-19

On May 5th, 2023, WHO declared an end to the global COVID-19 public health emergency, which means a significant transition from global critical emergency response activities to long-term sustained COVID-19 prevention and control. At this very moment, we make a comprehensive review on various control policies taken by 127 countries/territories during the first wave of COVID-19 pandemic until July 2nd, 2020, and evaluate their impacts on the epidemic dynamics in a quantitative way through both linear and nonlinear regressions. Through our analyses, the intrinsic correlations between the strength of control policies and the dynamical characteristics of COVID-19 epidemics are revealed not only for every country/territory under consideration, but also in a global view. Our results may help to design more economical and more effective preventive measures during the long-term fight against COVID-19 in the future.Comment: 17 pages, 5 figures, 2 table

Thermodynamics for reduced models of chemical reactions by PEA and QSSA

The partial equilibrium approximation (PEA) and the quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies have primarily focused on the accuracy of solutions before and after applying model reduction. In this paper, however, we adopt a thermodynamic view and aim to establish a quantitative connection on the essential thermodynamic quantities, such as entropy production rate, free-energy dissipation rate, and entropy flow rate, between the original chemical mass-action equations and the reduced models obtained by PEA or QSSA. Our findings reveal that the reduced models by PEA and QSSA may not preserve the thermodynamic structure of the original full model, particularly when algebraic relations are used instead of differential equations. This is evident in the loss of non-negativity of the free-energy dissipation rate. To validate our results, we apply them to the Michaelis-Menten reactions as a prototype, both analytically and numerically. We anticipate that our study will inspire a reevaluation of the effectiveness of various model reduction or approximation methods from the perspective of nonequilibrium thermodynamics