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In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. A dissipative process is a process in which energy (internal, bulk flow kinetic, or system potential) is transformed from some initial form to some final form; the capacity of the final form to do mechanical work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the second law of thermodynamics, the entropy varies with temperature (reduces the capacity of the combination of the two bodies to do mechanical work), but never decreases in an isolated system.

In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. A dissipative process is a process in which energy (internal, bulk flow kinetic, or system potential) is transformed from some initial form to some final form; the capacity of the final form to do mechanical work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the second law of thermodynamics, the entropy varies with temperature (reduces the capacity of the combination of the two bodies to do mechanical work), but never decreases in an isolated system.

在热力学中,<font color="#ff8000"> 耗散 dissipation</font>是在均匀热力学系统中发生的不可逆过程。耗散过程是能量(内能、整体流动动力学或系统势能)从某种初态转化为某种终态的过程，终态做机械功的能力小于初态做机械功的能力。例如，热传递是耗散的，因为它是内能从一个较热的物体向一个较冷的物体的转移。根据热力学第二定律，熵随温度变化(降低了两个物体组合做机械功的能力) ，但是在一个孤立的系统中熵从不减少。

在热力学中,<font color="#ff8000">耗散 dissipation</font>是在均匀热力学系统中发生的不可逆过程。耗散过程是能量(内能、整体流动动力学或系统势能)从某种初态转化为某种终态的过程，终态做机械功的能力小于初态做机械功的能力。例如，热传递是耗散的，因为它是内能从一个较热的物体向一个较冷的物体的转移。根据热力学第二定律，熵随温度变化(降低了两个物体组合做机械功的能力) ，但是在一个孤立的系统中熵从不减少。

These processes produce entropy (see entropy production) at a certain rate. The entropy production rate times ambient temperature gives the dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electrical current flow through an electrical resistance (Joule heating).

These processes produce entropy (see entropy production) at a certain rate. The entropy production rate times ambient temperature gives the dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electrical current flow through an electrical resistance (Joule heating).

这些过程以一定的速率产生熵（<font color="#ff8000"> 熵产生 entropy production</font>)。熵产生速率乘以环境温度就得到了耗散功率。不可逆过程的重要例子有: <font color="#ff8000"> 热流 heat flow</font>通过<font color="#ff8000"> 热阻 thermal resistance</font>，<font color="#ff8000"> 流体 fluid flow</font>流过流阻，扩散(混合) ，<font color="#ff8000"> 化学反应 chemical reactions</font>，<font color="#ff8000"> 电流 electric current</font>流过<font color="#ff8000"> 电阻 electrical resistance</font>(<font color="#ff8000"> 焦耳加热 joule heating</font>)。

这些过程以一定的速率产生熵（<font color="#ff8000">熵产生 entropy production</font>)。熵产生速率乘以环境温度就得到了耗散功率。不可逆过程的重要例子有: <font color="#ff8000">热流 heat flow</font>通过<font color="#ff8000">热阻 thermal resistance</font>，<font color="#ff8000">流体 fluid flow</font>流过流阻，扩散(混合) ，<font color="#ff8000">化学反应 chemical reactions</font>，<font color="#ff8000">电流 electric current</font>流过<font color="#ff8000">电阻 electrical resistance</font>(<font color="#ff8000">焦耳加热 joule heating</font>)。

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A particular occurrence of a dissipative process cannot be described by a single individual Hamiltonian formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction, and all similar forces that result in decoherency of energy&mdash;that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

A particular occurrence of a dissipative process cannot be described by a single individual Hamiltonian formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction, and all similar forces that result in decoherency of energy&mdash;that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

耗散过程的一个特殊现象不能用一个单独的<font color="#ff8000"> 哈密顿 Hamiltonian</font>形式来描述。耗散过程需要一组可容许的个体哈密顿量描述，确切地说，<font color="#32CD32">描述感兴趣的过程的实际特殊现象是未知的</font>。这包括摩擦力和所有导致能量[[消相干]]的类似力，即将<font color="#ff8000"> 相干性 coherent</font>或定向能量流转换为非定向或更<font color="#ff8000"> 各相同性 isotropic</font>的能量分布。

耗散过程的一个特殊现象不能用一个单独的<font color="#ff8000">哈密顿 Hamiltonian</font>形式来描述。耗散过程需要一组可容许的个体哈密顿量描述，确切地说，<font color="#32CD32">描述感兴趣的过程的实际特殊现象是未知的</font>。这包括摩擦力和所有导致能量[[消相干]]的类似力，即将<font color="#ff8000">相干性 coherent</font>或定向能量流转换为非定向或更<font color="#ff8000">各相同性 isotropic</font>的能量分布。

In [[computational physics]], numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [[advection]] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [[numerical stability]] characteristics of the solution.<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>

In [[computational physics]], numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [[advection]] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [[numerical stability]] characteristics of the solution.<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>

在<font color="#ff8000"> 计算物理学 computational physics</font>中，数值耗散（也称为“数值扩散”）是指微分方程数值解可能产生的某些副作用。当用数值近似方法求解无耗散的纯<font color="#ff8000"> 平流 advection</font>方程时，初始波的能量可以用类似于扩散过程的方式降低。这种方法被称为包含“耗散”。在某些情况下，故意添加“人工耗散”来改善解的<font color="#ff8000"> 数值稳定性 numerical stability</font>特性。<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>  

在<font color="#ff8000">计算物理学 computational physics</font>中，数值耗散（也称为“数值扩散”）是指微分方程数值解可能产生的某些副作用。当用数值近似方法求解无耗散的纯<font color="#ff8000">平流 advection</font>方程时，初始波的能量可以用类似于扩散过程的方式降低。这种方法被称为包含“耗散”。在某些情况下，故意添加“人工耗散”来改善解的<font color="#ff8000">数值稳定性 numerical stability</font>特性。<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>  

A formal, mathematical definition of dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set.

A formal, mathematical definition of dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set.

<font color="#ff8000"> 漫游集 wandering sey</font>文章中给出了在<font color="#ff8000"> 保测度动力系统 measure-preserving dynamical system</font>的数学研究中常用的耗散的形式化数学定义。

<font color="#ff8000">漫游集 wandering sey</font>文章中给出了在<font color="#ff8000">保测度动力系统 measure-preserving dynamical system</font>的数学研究中常用的耗散的形式化数学定义。