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→Stochastic methods
One approach to non-equilibrium statistical mechanics is to incorporate stochastic (random) behaviour into the system. Stochastic behaviour destroys information contained in the ensemble. While this is technically inaccurate (aside from hypothetical situations involving black holes, a system cannot in itself cause loss of information), the randomness is added to reflect that information of interest becomes converted over time into subtle correlations within the system, or to correlations between the system and environment. These correlations appear as chaotic or pseudorandom influences on the variables of interest. By replacing these correlations with randomness proper, the calculations can be made much easier.
One approach to non-equilibrium statistical mechanics is to incorporate stochastic (random) behaviour into the system. Stochastic behaviour destroys information contained in the ensemble. While this is technically inaccurate (aside from hypothetical situations involving black holes, a system cannot in itself cause loss of information), the randomness is added to reflect that information of interest becomes converted over time into subtle correlations within the system, or to correlations between the system and environment. These correlations appear as chaotic or pseudorandom influences on the variables of interest. By replacing these correlations with randomness proper, the calculations can be made much easier.
处理非平衡态统计力学的一个方法是将随机行为引入系统。随机行为可以破坏系综中包含的信息。虽然这在技术上是不准确的(除了涉及黑洞的假设情况外，黑洞系统本身不会导致信息丢失) ，但这种随机性是为了反映出，随着时间的推移，感兴趣的信息会在系统内部转化为微妙的相关性，或者系统与环境之间的相关性。这些关联表现为对感兴趣的变量的混沌或伪随机的影响。用适当的随机性取代这些相关性，计算可以变得容易得多。
|1 = Boltzmann transport equation: An early form of stochastic mechanics appeared even before the term "statistical mechanics" had been coined, in studies of kinetic theory. James Clerk Maxwell had demonstrated that molecular collisions would lead to apparently chaotic motion inside a gas. Ludwig Boltzmann subsequently showed that, by taking this molecular chaos for granted as a complete randomization, the motions of particles in a gas would follow a simple Boltzmann transport equation that would rapidly restore a gas to an equilibrium state (see H-theorem).
|1 = Boltzmann transport equation: An early form of stochastic mechanics appeared even before the term "statistical mechanics" had been coined, in studies of kinetic theory. James Clerk Maxwell had demonstrated that molecular collisions would lead to apparently chaotic motion inside a gas. Ludwig Boltzmann subsequently showed that, by taking this molecular chaos for granted as a complete randomization, the motions of particles in a gas would follow a simple Boltzmann transport equation that would rapidly restore a gas to an equilibrium state (see H-theorem).
玻尔兹曼输运方程: 在动力学理论研究中，早期的随机力学形式甚至在“统计力学”一词被创造之前就已经出现了。詹姆斯·克拉克·麦克斯韦已经证明分子碰撞会导致气体内部明显的混沌运动。路德维希·玻尔兹曼随后证明，如果把这种分子混沌理所当然地看作是一种完全的随机化，那么气体中粒子的运动将遵循一个简单的玻尔兹曼输运方程，这个方程将使气体迅速恢复到平衡状态(见 h 定理)。
玻尔兹曼输运方程: 在动力学理论研究中，早期的随机力学形式甚至在“统计力学”一词被创造之前就已经出现了。詹姆斯·克拉克·麦克斯韦已经证明分子碰撞会导致气体内部明显的混沌运动。路德维希·玻尔兹曼随后证明，如果把这种分子混沌理所当然地看作是一种完全的随机化，那么气体中粒子的运动将遵循一个简单的玻尔兹曼输运方程，这个方程将使气体迅速恢复到平衡状态(见H-定理)。
The Boltzmann transport equation and related approaches are important tools in non-equilibrium statistical mechanics due to their extreme simplicity. These approximations work well in systems where the "interesting" information is immediately (after just one collision) scrambled up into subtle correlations, which essentially restricts them to rarefied gases. The Boltzmann transport equation has been found to be very useful in simulations of electron transport in lightly doped semiconductors (in transistors), where the electrons are indeed analogous to a rarefied gas.
The Boltzmann transport equation and related approaches are important tools in non-equilibrium statistical mechanics due to their extreme simplicity. These approximations work well in systems where the "interesting" information is immediately (after just one collision) scrambled up into subtle correlations, which essentially restricts them to rarefied gases. The Boltzmann transport equation has been found to be very useful in simulations of electron transport in lightly doped semiconductors (in transistors), where the electrons are indeed analogous to a rarefied gas.
玻耳兹曼输运方程及其相关方法是非平衡态统计力学的重要工具，因为它们极其简单。这些近似方法在“感兴趣的”信息立即(在一次碰撞之后)变成微妙关联的系统中非常有效，这种关联本质上限制它们为稀薄气体。玻耳兹曼输运方程被发现在模拟轻掺杂半导体(晶体管)的电子输运中非常有用，其中的电子确实类似于稀薄气体。
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=== Near-equilibrium methods ===
=== Near-equilibrium methods ===