\[A = U - TS,\qquad \Delta A_{T,V} \le 0\ (\text{自发}),\qquad w_\text{max} = \Delta A\ (\text{恒温})\]\[A = U - TS,\qquad \Delta A_{T,V} \le 0\ (\text{spontaneous}),\qquad w_\text{max} = \Delta A\ (\text{const. T})\]
含义Meaning
恒温恒容下判断自发方向的状态函数；恒温过程中体系能做的最大总功等于 −ΔA（所以又称“功函”）。统计力学中与正则配分函数直接相联：A = −kT ln Q。
The criterion at constant T and V; −ΔA is the maximum total work at constant temperature (hence ‘work function’). Statistically A = −kT ln Q.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(A\) | 亥姆霍兹能Helmholtz energy | J |
推导Derivation
恒温下 \(dA = dU - TdS\)；由克劳修斯不等式 \(TdS \ge \delta q\)，得 \(dA \le \delta w\)。
At constant T, dA = dU − TdS ≤ δw.
恒容且无非体积功时 δw = 0，所以 dA ≤ 0。
At constant V with no other work, dA ≤ 0.
适用条件与局限Assumptions & limitations
化学中恒压更常见，多用 G；但固体、恒容反应器和统计力学中 A 更自然。
G is usually more convenient in chemistry.