自由能的内在本质
胡良
深圳市宏源清实业有限公司
摘要：亥姆霍兹自由能（自由能），是物理学中的一个热力学参数，等于内能减去绝对温度与熵的乘积，揭示了一个可逆等温等容过程的最大功输出的内涵。
关键词：亥姆霍兹自由能，吉布斯自由能 ，背景空间，温度，熵，不确定性原理
作者：总工，高工，硕士，副董事长
1亥姆霍兹自由能
亥姆霍兹自由能（自由能），是物理学中的一个热力学参数，等于内能减去绝对温度与熵的乘积，揭示了一个可逆等温等容过程的最大功输出的内涵。
Helmholtz free energy (free energy) is a thermodynamic parameter in physics, equal to the product of internal energy minus absolute temperature and entropy, and reveals the connotation of the maximum work output of a reversible isothermal and isometric process.
其表达式为：A=U-TS，其中，
A，表达亥姆霍兹自由能（自由能），量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
U，表达系统的内能，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
T，表达温度，量纲，[L^(2)T^(-3)]；
S，表达熵，量纲，[L^(3)T^(0)]。
此外，亥姆霍兹自由能（自由能）的微分表达式为：
dA=-SdT-PdV+μdN,其中，
P，表达压强，量纲，[L^(2)T^(-3)]；
V，表达体积，量纲，[L^(3)T^(0)]；
μ,表达化学势，每个基本粒子的平均吉布斯自由能 ，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
N，表达粒子数，量纲，[L^(0)T^(0)]。
The expression is: A=U-TS, where,
A, express Helmholtz free energy (free energy), dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
U, the internal energy of the expression system, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
T, expressing temperature, dimension, [L^(2)T^(-3)];
S, expression entropy, dimension, [L^(3)T^(0)].
In addition, the differential expression of Helmholtz free energy (free energy) is:
dA=-SdT-PdV+μdN, where,
P, expression pressure, dimension, [L^(2)T^(-3)];
V, expression volume, dimension, [L^(3)T^(0)];
μ, expressing the chemical potential, the average Gibbs free energy of each elementary particle, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
N, expressing the number of particles, dimension, [L^(0)T^(0)].
更进一步来看，自由能是系统内能的一部分，而这部分（自由能）在可逆等温过程中，可被转化成功。在粒子数不变的等温过程中，系统对外界所做的功一定只能小于（或等于）其自由能的减少，也就是说，系统自由能的减少就是等温过程中系统对外界所做的最大功。
Looking further, free energy is part of the internal energy of the system, and this part (free energy) can be converted successfully in the reversible isothermal process. In an isothermal process where the number of particles is constant, the work done by the system to the outside world must be less than (or equal to) the reduction of its free energy, that is, the reduction of the system's free energy is what the system does to the outside world during the isothermal process Maximum work.
最大功定理可表达为：Aa - Ab ≥ -W，其中，
Aa，系统起始点的亥姆霍兹自由能，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
Ab ，系统终点的亥姆霍兹自由能，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
表达功，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
如果是等温等容过程，W=0，则有，Aa - Ab ≥ 0。
The maximum work theorem can be expressed as: Aa-Ab ≥ -W, where,
Aa, Helmholtz free energy at the starting point of the system, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
Ab, the Helmholtz free energy at the end of the system, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
Express work, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
If the process is isothermal and isovolumic, W=0, yes, Aa-Ab ≥ 0.
从广义的角度来看，
当，ΔA=Aa - Ab<0,时，体现了过程是一个自发过程；
当，ΔA=Aa - Ab=0,体现了过程是一个可逆过程（或系统处于平衡态）；
当，ΔA=Aa - Ab0>0,体现了过程是一个不可能发生的过程，或者说，背景空间（环境）给予该系统补充内能。
From a broad perspective,
When ΔA=Aa-Ab<0, it shows that the process is a spontaneous process;
When, ΔA=Aa-Ab=0, it shows that the process is a reversible process (or the system is in equilibrium);
When, ΔA=Aa-Ab0>0, it means that the process is an impossible process, or that the background space (environment) gives the system supplemental internal energy.
根据量子三维常数理论，h*C=Vp*C^(3)，由于该系统与背景空间（环境）构成了整个宇宙。亥姆霍兹自由能（A）揭示了该系统与背景空间（环境）的相互联系。
According to the quantum three-dimensional constant theory, h*C=Vp*C^(3), because the system and the background space (environment) constitute the entire universe. Helmholtz free energy (A) reveals the interconnection between the system and the background space (environment).
例如，孤立量子体系的大爆炸，体现为，ΔA=Aa - Ab<0,时，表达了相对于背景空间（环境），其过程是一个自发过程。而，孤立量子体系的大收缩，体现为，ΔA=Aa - Ab>0,时，表达了相对于背景空间（环境），其过程是背景空间（环境）给予该系统补充内能。孤立量子体系处于平衡态，体现为，ΔA=Aa - Ab=0,时，表达了相对于背景空间（环境），系统处于平衡态（可逆）过程。
For example, the big explosion of an isolated quantum system is expressed as: ΔA=Aa-Ab<0, expressing that the process is a spontaneous process relative to the background space (environment). However, the large contraction of the isolated quantum system is reflected in that when ΔA=Aa-Ab>0, it expresses that relative to the background space (environment), the process is that the background space (environment) gives the system supplemental internal energy. The isolated quantum system is in equilibrium state, when ΔA=Aa-Ab=0, it expresses that the system is in equilibrium state (reversible) process relative to the background space (environment).
显然，如果宇宙是一个孤立量子体系，则其背景空间是绝对真空，则宇宙大爆炸理论成立；体现了宇宙具有确定性。
如果宇宙是无限大的，则对于一个孤立量子体系来说，其背景空间就不可能是真空，则宇宙大爆炸理论不成立。根据量子三维常数理论，h*C=Vp*C^(3)，不确定性原理（量子力学）是正确的，可见宇宙是无穷大的。
Obviously, if the universe is an isolated quantum system, and its background space is an absolute vacuum, the theory of the Big Bang is established; it shows that the universe is deterministic.
If the universe is infinitely large, for an isolated quantum system, the background space cannot be a vacuum, and the theory of the Big Bang does not hold. According to the quantum three-dimensional constant theory, h*C=Vp*C^(3), the principle of uncertainty (quantum mechanics) is correct, and it can be seen that the universe is infinite.
2亥姆霍兹自由能（A）与吉布斯自由能 （G ）的联系
吉布斯自由能 （G ）可以表达为，
G = A + pV=H-TS，其中，
G，吉布斯自由能，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
A，亥姆霍兹自由能，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
P ，压强，，量纲，[L^(2)T^(-3)]；
V，表达体积，量纲，[L^(3)T^(0)]；
H，表达焓，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
T，表达温度，量纲，[L^(2)T^(-3)]；
S，表达熵，量纲，[L^(3)T^(0)]。
而，吉布斯自由能（G），G = μN；
可见，亥姆霍兹自由能（A），A= μN - pV。
Gibbs free energy (G) can be expressed as,
G = A + pV=H-TS, where,
G, Gibbs free energy, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
A, Helmholtz free energy, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
P, pressure, dimension, [L^(2)T^(-3)];
V, expression volume, dimension, [L^(3)T^(0)];
H, expression enthalpy, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
T, expressing temperature, dimension, [L^(2)T^(-3)];
S, expression entropy, dimension, [L^(3)T^(0)].
However, Gibbs free energy (G), G = μN;
It can be seen that the Helmholtz free energy (A), A = μN-pV.
吉布斯自由能 （G ）的变化，可作为恒温及恒压过程中，自发与平衡的判据。
这意味着，亥姆霍兹自由能（功函）是在等温条件下，相对于背景空间（环境），具有的做功的能力。
吉布斯自由能 （G ），除体积功之外，在等温等压的条件下，相对于背景空间（环境），具有的做功的能力。
The change of Gibbs free energy (G) can be used as a criterion for spontaneous and equilibrium in the process of constant temperature and constant pressure.
This means that Helmholtz free energy (work function) is the ability to do work with respect to the background space (environment) under isothermal conditions.
Gibbs free energy (G), in addition to volume work, has the ability to do work relative to the background space (environment) under isothermal and isobaric conditions.
3统计物理学中的亥姆霍兹自由能（A）
对于统计物理学来说，亥姆霍兹自由能（A）与配分函数（Z）具有直接联系，其表达式：A= -N*K*T*lnZ，其中，
K，表达玻尔兹曼常数，量纲，[L^(3)T^(0)]；
T，表达温度，量纲，[L^(2)T^(-3)]；
lnZ，表达配分函数，量纲，[L^(0)T^(0)]；
表达粒子数量，量纲，[L^(0)T^(0)]。
For statistical physics, Helmholtz free energy (A) is directly related to the partition function (Z), and its expression is: A= -N*K*T*lnZ, where,
K, express Boltzmann constant, dimension, [L^(3)T^(0)];
T, expressing temperature, dimension, [L^(2)T^(-3)];
lnZ, expression partition function, dimension, [L^(0)T^(0)];
Express the number of particles, dimension, [L^(0)T^(0)].
4内能的本质
对于热力学系统的绝热过程，外界对系统所做的功是由过程的起始状态及终点状态决定，而不依赖于做功的具体过程及方式。
任何一个热力学系统都一定存在一个只依赖于系统自身状态的物理量，这个物理量在两个状态间的差别与外界在绝热过程中对系统所做的功相联系。
功能够表达能量变化的量度，因此，这个物理量一定是系统的一种能量（系统的内能）。
For the adiabatic process of a thermodynamic system, the work done by the outside world on the system is determined by the starting state and the end state of the process, and does not depend on the specific process and method of doing work.
Any thermodynamic system must have a physical quantity that depends only on the state of the system. The difference between the two physical states is related to the work done by the outside world on the system during the adiabatic process.
Work can express a measure of energy change, so this physical quantity must be an energy of the system (internal energy of the system).
当系统从状态（a）经过绝热过程达到状态（b）时，内能的增加量可表达为，△U=Ub-Ua；其等于外界（背景空间）对系统所做的功W，即，W=ΔU。
在力学中，重力对物体所做的功是由起点位置及终点位置决定，而与物体具体的运动路径无关。也就是说，物体在两位置之间的重力势能之差，就是物体在这两个位置之间移动时，重力所做的功。
When the system reaches the state (b) from the state (a) through the adiabatic process, the increase in internal energy can be expressed as △U=Ub-Ua; it is equal to the work W done by the outside world (background space) to the system, ie, W=ΔU.
In mechanics, the work done by gravity on an object is determined by the start and end positions, and has nothing to do with the specific path of the object. That is to say, the difference in the potential energy of gravity between two positions of an object is the work done by gravity when the object moves between these two positions.
从另一个角度来看，U=A+TS；其中，
U，表达系统的内能，量纲，[L^(3)T^(-1)]*[L^(2)T^(-2)]；
T，表达温度，量纲，[L^(2)T^(-3)]；
S，表达熵，量纲，[L^(3)T^(0)]。
这意味着，系统的内能属于系统的内禀属性，而内能的改变与背景空间（环境）有关。
From another perspective, U=A+TS; where,
U, the internal energy of the expression system, dimension, [L^(3)T^(-1)]*[L^(2)T^(-2)];
T, expressing temperature, dimension, [L^(2)T^(-3)];
S, expression entropy, dimension, [L^(3)T^(0)].
This means that the internal energy of the system belongs to the intrinsic attribute of the system, and the change of the internal energy is related to the background space (environment).
