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The essential contribution to the thermodynamics of the non-equilibrium systems was brought by Prigogine, when he and his collaborators investigated the systems of chemically reacting substances. The stationary states of such systems exists due to exchange both particles and energy with the environment. In section 8 of the third chapter of his book, Prigogine has specified three contributions to the variation of entropy of the considered system at the given volume and constant temperature <math> T</math> . The increment of entropy <math> S</math> can be calculated according to the formula  

The essential contribution to the thermodynamics of the non-equilibrium systems was brought by Prigogine, when he and his collaborators investigated the systems of chemically reacting substances. The stationary states of such systems exists due to exchange both particles and energy with the environment. In section 8 of the third chapter of his book, Prigogine has specified three contributions to the variation of entropy of the considered system at the given volume and constant temperature <math> T</math> . The increment of entropy <math> S</math> can be calculated according to the formula  

对非平衡系统热力学的最重要贡献是由普利高津给出的，当时他和他的合作者研究了化学反应物质系统。由于粒子和能量与环境的交换，这类系统的静止状态是存在的。在他的书的第三章的第8节中，普里高金详细说明了在给定的体积和恒定的温度下，被考虑系统的熵的变化有三个贡献。根据该公式可以计算出熵的增量 s </math >  

对非平衡系统热力学的最重要贡献是由普利高津做出的，当时他和他的合作者研究了化学反应物质系统。由于与环境交换粒子和能量，这类系统的定态是存在的。在他的书的第三章的第8节中，普利高津详细说明了在给定体积和恒定温度<math> T</math> 下，被考虑系统的熵的变化有三种贡献。根据该公式可以计算出熵<math> S</math>的增量

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The first term on the right hand side of the equation presents a stream of thermal energy into the system; the last term—a stream of energy into the system coming with the stream of particles of substances <math> \Delta N_\alpha </math> that can be positive or negative, <math> \mu_\alpha</math> is chemical potential of substance <math> \alpha</math>. The middle term in (1) depicts energy dissipation (entropy production) due to the relaxation of internal variables <math> \xi_j</math>. In the case of chemically reacting substances, which was investigated by Prigogine, the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalised, to consider any deviation from the equilibrium state as an internal variable, so that we consider the set of internal variables <math> \xi_j</math> in equation (1) to consist of the quantities defining not only degrees of completeness of all chemical reactions occurring in the system, but also the structure of the system, gradients of temperature, difference of concentrations of substances and so on.

The first term on the right hand side of the equation presents a stream of thermal energy into the system; the last term—a stream of energy into the system coming with the stream of particles of substances <math> \Delta N_\alpha </math> that can be positive or negative, <math> \mu_\alpha</math> is chemical potential of substance <math> \alpha</math>. The middle term in (1) depicts energy dissipation (entropy production) due to the relaxation of internal variables <math> \xi_j</math>. In the case of chemically reacting substances, which was investigated by Prigogine, the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalised, to consider any deviation from the equilibrium state as an internal variable, so that we consider the set of internal variables <math> \xi_j</math> in equation (1) to consist of the quantities defining not only degrees of completeness of all chemical reactions occurring in the system, but also the structure of the system, gradients of temperature, difference of concentrations of substances and so on.

方程式右边的第一项代表了进入系统的热能流; 最后一项ーー进入系统的能量流，伴随着粒子流进入系统，粒子流可以是正的也可以是负的。第一部分的中期描述了由于内部变量的松弛而引起的能量耗散(产生熵)。在化学反应物质的情况下，由普利戈金研究，内部变量似乎是测量不完全的化学反应，也就是测量多少考虑的体系与化学反应是不平衡的。这个理论可以推广，把任何偏离平衡态的情况看作是一个内变量，因此我们认为方程式(1)中的内变量集合不仅包含了定义系统中所有化学反应完全程度的量，而且还包含了系统的结构、温度梯度、物质浓度差等。

方程式右边的第一项代表进入系统的热能; 最后一项为伴随着粒子进入系统而带来的能量流，粒子流<math> \Delta N_\alpha </math>可以是正的也可以是负的，<math> \mu_\alpha</math> 是物质<math> \alpha</math>的化学势。方程右边中间项描述了由于内部变量<math> \xi_j</math>的弛豫而引起的能量耗散(熵产生)。在普利高津研究的化学反应物质的情况下，内部变量看起来是测量化学反应的未完成度，也就是测量考虑的化学反应体系远离平衡的程度。这个理论可以推广，把任何对平衡态的偏离看作是内部变量，因此我们认为方程式(1)中的内部变量集合<math> \xi_j</math>不仅包含了定义系统中所有化学反应完成程度的量，而且还包含了系统的结构、温度梯度、物质浓度差等。

==Flows and forces==

==Flows and forces==