Thermodynamics For Long-distance Interaction System

Abstract: Firstly the obstacle of thermodynamics for long-distance interaction system is introduced in this article. Then the second law of thermodynamics is applied to the long-distance interaction system and we get that it is not suitable for long-distance interaction system. And the unbalanced Brown movement with balanced static electricity is analyzed.

0、Introduction:

The following are statements of thermodynamics system under gravitation.
1、L.D.Landau, theoretical physicist in former Soviet Union, stated that gravitation effect is critical especially in astrophysics. Gravitation on thermodynamics is like outside noise affecting a system, and it is unstable. Uniformly distributed substance can turn into clusters, which is not uniform, due to gravitation. Thus most part of the actual vast universe is far from balanced state.
-----From “Entropy”,Science Publishing Firm, by Duan Feng and others, 1992.9Ρ.101
2、Though Einstein’s general theory of relativity and the space curve in it somehow showed nature of gravity. Things become complicated when talking about gravity order. Currently there is no agreed view or idea on thermodynamics of systems under gravitation. For example, the concept of entropy of gravity field is still not clear and there is not clear expression for it.
When the gravity is little enough to be negleted, the gas tends to be uniform. While under gravity, it will concentrate and won’t be uniform.
-----From “God And New Physics” Hunan Technology Publishing Firm, 1996.10, Ρ.194
written by Polo Davis in UK, translated by Pei Xu
The above question also exists in charged system. For a conductor with balanced static charges, the charges can only distribute on limited surface(expression of order and definite location). The conclusion of the second law of thermodynamics is supposed to be that charges should divert as much as possible(to make entropy maximum).
The following discussion will show that the second law of thermodynamics is not suitable for long-distance interaction system.

1、The logic conflict of the second law of thermodynamics

The description of the second law of thermodynamics is that the thermal activity of an independent system always make entropy increase and make it maximum(stable balance)
There is some requirement for the subject of the second law of thermodynamics, which is independent system. While for the following independent system, there are problems when the second law of thermodynamics is applied. There are two cups A and B of water on the table. There are many floating charges. The outside doesn’t have any effect on them. So overall they can be viewed as independent system. From the second law of thermodynamics, the system should have a stable balanced state. From part like A, It is affected by B’s charges. So it cannot be viewed as independent system. And it is a big question whether it has a stable state or not. The same applies to B. Same subject and different conclusions show that the theory has disadvantage when applied to such subject.
Whether the system has stable state or not, should be determined by physical equations which should includes heat and electricity.
1 Poisson Equation
2 Boltzman Equation ρ=A*exp（qu/kT）
It is hard to solve the equations. They are not linear. From instinct, the probability of that they can be solved is very small.
It shows the second law of thermodynamics is only practical when there is not long-distance system. For example, there two internal combustion engines working in a classroom. The interaction between them is universal gravitation, which is too small and the effect of it can be negleted.
But the universal gravitation between celestial bodies cannot be negleted. It will also ruin the independence inside a system. Any galaxy is affected by other galaxies. So the second law of thermodynamics is not suitable anymore. Theory of heat death of cosmos is practically meaningless.
The above is obstacle of language and logic. The following two parts of discussion is on problems of calculation.

2、Problem of Planck’s entropy theory for long-distance interaction system

Most contribution of Planck was on quantum physics. But he had his own view in thermodynamics. And it became part of classical thermodynamics.
The following is deduction of probability in thermodynamics. Planck found that there is monotonic change between entropy of independent system and probability in thermodynamics. He guessed that there is some relation as the following between the entropy and the probability.
S=f（W）
Suppose there are two independent parts in this system,
S------- Entropy of the system
S1----- Entropy of part 1
S2------- Entropy of part 2
W------- Overall Probability
W1----- Probability of part 1
W2----- Probability of part 2
Suppose S=S1+S2=f（W）
S1=f（W1）
S2=f（W2）
W=W1*W2
Through infinitesemal calculus, we get
S=k*In（W）----------（2）
See “Statistical Physics Introduction” the second edition by Zhuxi Wang

Probability relation W=W1*W2 requires the two parts are independent. Can all subjects meet the requirement? Actually there is something that breaks their independency. For example, there are two cups of water on a table. (which can be viewed as two parts of the system, the segmentation is random) there are a lot of charges floating there, so there is long-distance interaction, so independency is meaningless here. There is shortage in Planck deduction.
S=k*In（W）is an important core formula in thermodynamics. That there is some mistake in its deduction means there should be some adjustment for the original thermodynamics.

3、The equation H=G+ST is not correct under the condition of remote-interaction system.
The second law of thermodynamics shows that there is some constraint condition in the process of heat energy’s transform into function, which is that heat energy can be divide into two parts: the ordered energy ( can be transformed into function) and disordered energy( can’t be transformed into function).
This is H=G+ST
Suppose a system whose different parts have different temperature, which is the common analysis by physics who often divide the system into many little parts and each parts’ temperature is think as the same, then the above formulation can be rewritten as the following.
h=g+s*T
Using g and s is very common in the advanced theory of thermodynamics. Even if the temperature is the same everywhere, using the equation h=g+s*T, is more correct, because it maintain the continuity of physical law.
Now let us image an object with electricity and each parts are interacted with others by the remote electromagnetic, it is natural that electromagnetic energy doesn’t belongs to any local part. In this system, we can’t divide it into many parts, but the temperature has the local part’s characteristic. So the formulation h=g+s*T can’t be applied. This has essentially broken the world of ordered energy and disordered energy.

4、 Research of static electric balance

The charge distribution on the surface of conductor is not uniform. From diffusion effect, the current exists. The diffusion can affect the charge distribution. And the temperature can affect diffusion, thus it can affect the charge distribution. So the charge distribution is different when the temperature is 30 degree comparing to that when it is 50 degree. The distribution of constant potential of charges is unique and cannot vary with temperature. So the theory of is meaningless.
If there is only diffusion current , the charge distribution will be uniform. Actually it is not that way. There is some corresponding movement inside for sure. Previously we deduced that there is potential difference on charged conductor. The potential difference can drive the current (see the following figure) and diffusion current “balanced”. Such mechanism also exists in the PN knot of Semiconductor.
there are two forms of current of field of force
J=r*E+u*f*ρ
It is the combination of two experimental laws. Then diffusion is considered. The Brown movement on charged conductor is(see figure 1)
J=-D*dρ/dx+r*E+u*f*ρ

Web of "figure 1" is "http://photo.163.com/openpic.php?user=zbl1905&pid=147836835&_dir=%2F1386442";

Figure 1 Thermodynamic figure of static electric balance

Usually D,ρ,dρ/dx is small and r is big, so E and f are small. The theory of constant potential has only engineering meaning, which is approximate.
The electric lines of force and electric field exist not only on the surface of a conductor. The electric lines of force can penetrate inside of the conductor. Inside the conductor, ρ tends to be 0. So
J=r*E
Conducting current will produce heat. Thus the inside temperature of the conductor will be a little higher than the surface.
If it is just a cup of water on a table, we see stable balance. For charged conductor, figure 1 shows much heat transmission which can be observed. It is reasonable with the precedent theoretical background.
Einstein introduced two kinds of thermal activities when he studied Brown movement in a field of force.
J=-D*dρ/dx+u*f*ρ
Considering Eistein Equation, we get
J=-u（kT *dρ/dx+f*ρ）
When J=0,the system is balanced, we get
ρ=A*exp(-Ep/kT)
For charged conductors, there are transmission factors D, u, and r. If there is only Einstein equation, the transmission factors cannot be extracted. The barely got balanced distribution will contain transmission factors of thermodynamics for sure(macro and micro thermodynamic transmission is not avoidable). And canonical distribution
ρ=A*exp(-E/kT)
only has direction relation with energy. From thermodynamic transmission, charged conductor does not support statistical mechanics with canonical distribution.

6、End
The second law of thermodynamics is suitable only for independent system inside which each part should be relatively independent. Only ideal gas meets the requirement strictly.
For real gas, the interaction of molecules ruin the independency. How bad does it ruin? It needs further observation. But the problem is discovered.

6.1、Carnot Calculation
Carnot circulation and carnot efficiency are the base for the second law of thermodynamics. Now the equations of state and energy conservation are used to calculate the efficiency.
PV=nRT
DE=Q-W
E=xRT (x=1.5、2.5。。。)
Get
η=1-T1/T2
For real gas
{P-A(V，T)}{V-B（V，T）}=nRT
DE=Q-W
E=E（V，T）
Our theoretical expected value is
η=1-T1/T2
From complex theory, the simple conclusion comes. It can not be imagined in mathematical practice. While different gases have different states, there is some doubt when one Carnot efficiency is used to include all of them. Further confirmation is needed.
If there is any break, the practice of thermodynamics is not confined by the second law of thermodynamics anymore.