# Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics

## Abstract

**:**

## 1. Introduction

## 2. Basics of Nonequilibrium Thermodynamics

**B**, the situation is slightly different, as suggested in the 1945 Onsager-Casimir relation ${L}_{jk}(\mathbf{B})={L}_{kj}(-\mathbf{B})$ [5]. The reciprocal relations decrease by half the number of all transport coefficients, which should be found to fully describe the system evolution. Only when a specific physical model is suggested can the nonequilibrium thermodynamics provide a clue as to what the sign and value of transport coefficients are. The problem is that without knowledge of all transport coefficients based only on linear thermodynamics, it is challenging to derive even classical equilibrium equations.

## 3. Basic Equation of Physicochemical Mechanics and Generalization of the Second Law of Thermodynamics

_{i}gives macroscopic forces acting on particles “i”. This leads to directed transport and, in a condensed medium, energy dissipation due to friction. According to theoretical mechanics, the evolution of any multicomponent system with friction may be described by Lagrange’s equation with an additional Rayleigh’s dissipation function $\dot{Q}$ [13]:

## 4. General Equation for Chemical Flux

_{i}, which has the units of velocity/molar force.

## 5. Diffusion, Other Transport Laws, and Their Equilibrium

^{−9}m

^{2}/s, which corresponds to mobility $U\approx 4\times {10}^{-13}\frac{\mathrm{m}}{\mathrm{s}}\cdot \frac{\mathrm{m}\mathrm{o}\mathrm{l}}{\mathrm{N}}$.

^{3}mol/m

^{3}(1 mole/L), using the value for ${U}_{i}$

_{,}the specific electrophoretic mobility induced by both monovalent ions should be $\sim 8\times {10}^{-5}\mathrm{m}\mathrm{o}\mathrm{l}/\mathrm{s}\cdot \mathrm{m}\cdot \mathrm{V}$, which agrees with the experiments. Taking one term in physicochemical potential after another, we will get other transport laws and the values of related transport coefficients.

## 6. Colloid Materials

## 7. Thermodiffusion

_{T}has the dimension 1/K.

## 8. Onsager’s Reciprocal Relations

^{2}F

^{2}UAc).

## 9. Dissipation and Thermodynamic Efficiency

## 10. Summary

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Kocherginsky, N.M.
Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics. *Entropy* **2023**, *25*, 1332.
https://doi.org/10.3390/e25091332

**AMA Style**

Kocherginsky NM.
Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics. *Entropy*. 2023; 25(9):1332.
https://doi.org/10.3390/e25091332

**Chicago/Turabian Style**

Kocherginsky, Nikolai Meerovich.
2023. "Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics" *Entropy* 25, no. 9: 1332.
https://doi.org/10.3390/e25091332