When define heat engine efficiency η as: η= W/ W1 , that is, replacing Q1 in the original definition η=W/ Q1 with W1 , W still is the net work the heat engine applied to the outside in one cycle,W1 is the work the heat engine applied to the outside in the cycle,let the element reversible cycle be Stirling cycle , if ∮dQ/T =0 is tenable,we can prove ∮dW/T =0,∮dE/T =0 !
If ∮dQ/T=0, ∮dW/T=0 and ∮dE/T=0 really define new system state variables, the three state variables are inevitably different from each other; on the other side, their dimensions are the same one, namely J/K, and they are all state variables. So, we have to “make” three different system state variables with same dimensions, and we don’t know what they are, no doubt, this is absurd.
In fact , replaceing ΔQ with dQ is taking for granted, if only we review the definition of differential, we know that the prerequisite of differential is there is a derivability function as y=f(x), however,there is not any function as Q=f(T) here at all, so, ΔQ can not become dQ.
On the other side, when ΔQ→0, lim(ΔQ/T)=0 but not lim(ΔQ/T)= dQ/T.
So, ∮dQ/T=0、∮dW/T=0 and ∮dE/T=0 are untenable at all !
The whole paper:
http://www.researchgate.net/profile/Shufeng_Zhang/blog/5007_EntropyA_concept_that_is_not_Physical_Quantity
http://wenku.baidu.com/view/cd8704d5b9f3f90f76c61b82.html
http://content.yudu.com/Library/A1pkpi/EntropyAconceptthati/resources/index.htm?referrerUrl=http%3A%2F%2Fwww.yudu.com%2Fitem%2Fdetails%2F234797%2FEntropy---A-concept-that-is-not-Physical-Quantity
Ah, I like it.
So what you are saying, is that while something like the second law of thermodynamics exists, the Boltzman definition of Entropy as disorder is incorrect and the mathematics on which that definition is based, is suspect due to some sleight of hand that doesn't hold up to mathematical rigor.
This would jibe with my interpretation that far from disorder, entropy is the flip side of the observation that energy flows from areas of highest potential to areas of lowest potential, and that relative order/disorder is a function of the energy/entropy balance, and is therefore reversable, except in a system that conserves entropy in an increasing energy supply.
hehe, in fact, it is not the so called “entropy”, it is another theory. Second law of thermodynamics is correct, but entropy is wrong.
Ah, but how can you say that, when the second law of thermodynamics requires equilibrium, and Uncertainty implies that equilibrium is impossible.
If you look closely at the second law of thermodynamics, it clearly requires that systems return to a state of equilibrium.
Equilibrium however is a Newtonian Concept that does not translate well into a Quantum Universe.
The more accurate you become, the more that you find that equilibrium is replaced not with a static state, but with a strange attractor, where the exact location is uncertain, but it tends to average out to a single location called the attractor. If we chose to call that location equilibrium we find that more often than not, it is never actually reached. Instead we must define equilibrium as a dynamic state attracted to the equiilibrium point.
To illustrate, if you hang a pendulum straight down, and use an acurate enough measurement, you will find that the pendulum is never completely still, it is always moving. What then is equilibrium?
Allow me to present my idea of what an entropy is:
For a system in equilibrium it can be in any one of the N states, then the probability of the system having energy En is Pn = (1/Q)exp(-En/kT), where Q = Sum [ exp(-En/kT) ] the summation is over n states (n=1,2,3..N)
k = Boltzmann’s constant, and T = temperature in Kelvin Q is called the partition function.
The entropy is then defined as
S = -k Sum x log x
where x = Pn .
(RP Feynman 1972 “Statistical Mechanics: A set of lectures sponsored by Huges Aircraft Research Laoratories” ,Reading Massachusatts:Benjamin)
More physically we take the specific heat of solids as [supported by observation of the values of specific heats of solids such as lead,aluminium,silicon and diamond ] comprising the lattice contribution c[aT^3 ] and the electronic contribution [bT]:
C = aT^3 +bT
The above shows that not only does the specific heat of the whole system tend to zero but the lattice and the electronic contributions vanish independently. This allows the use of absolute zero as a reference level for all thermodynamic calculations . The definition of entropy based on the Second Law is S(T)-S(0) = Integral(0 to T) [CdT/T], Since the specific heat tends to zero S(0)=0 and the Third Law allows us a unique value to the entropy at any other temperature viz
S(T) = Integral(0 to T) [CdT/T]
The concept of entropy inherent in the Second Law may be used to predict the behavior of the systems irrespective of its statistical significance. The Third Law requires us to think of entropy as a statistical and as well as a thermodynamic function. The Second Law merely postulates the existence of an entropy function, while the Third Law discusses its behavior.
(J Wilks 1961 “The Third Law of Thermodynamics” Oxford:OUP )
The Third Law makes our transition to quanum mechanical calculations possible. Taking |i> as a state with energy Ei and P as a quantum mechanical operator for a physical observer , then the expectation value or the average value of the observable is
= (1/Q) Sum(over |i>)[ exp(-Ei/kT)]
[Notation used: Integral (0 to a ) dx/x = log a ; Sum [ exp(-En/kT) ] = exp(-E1/kT) + exp(-E2/kT) + exp(-E3/kT) +…… +EN/kT ) ]
One may thus conclude that it is indeed a valid physical concept in physical chemistry, condensed state physics etc . It also features as an important ingredient of quantum cosmology and black hole physics.
Don't forget Dark Energy Physics as well, in its role as the inverse of the tendency of energy to flow from locations of highest potential to areas of lowest potential, it defines a distributive force that might define the nature of the Dark Energy postulated to make up 70% of the Universes energy supply.
True.
The confusion arises I believe due to the Shannon entropy (more mathematical ?) which can be related to thermodynamic entropy(more physical ?).
In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by an applied mathematician Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication".
The term information now has a new and vibrant meaning in fundamental physics and not really understood even by the so called experts in the spirit in which Feynman claimed "nobody actually understands quantum mechanics"!!
String theorists like Ed Witten have written highly illuminating articles on information which are worth reading and worth referring to!
The two concepts may not be as far apart as you think, if Wolfram's class 4 cellular automata are at all indicative. What we might find, is that uncertainty and order are both constrained by entropy. Any attempt to build too much uncertainty will result in infusion of order, and any attempt to build too much order will result in uncertainty due to these constraints. this is why a science that is based on too much certainty may be actually impossible to create. A more rational approach although not in the Western tradition would be to accept uncertainty and build it's acceptance into the science, by understanding the constraints on order and uncertainty. At any point in time, the energy/entropy balance will favor a constraint on both order and uncertainty that can be predicted according to the expansion of the Universe, and the supply of new energy flowing into the Universe.
It should therefore be possible to predict the precipitation of order during inflation.
I think we ought to get our definitions correct first!
Here are some definitions of the related terms that I find reasonable but not so enlightening. Any better offers?
"entropy"
Entropy amount of information about the microscopic motion of atoms making up the system which is not determined by a description of the macroscopic state of that system.
"equilibrium"
A system is said to be in thermodynamic equilibrium when it has maximum possible amount of entropy.
"Beckenstein bound"
The relationship between the area of a surface and the maximum amount of information about the universe on one side of it that can pass through it to an observer on the other side. The relationship states that the number of bits of information the observer can gain cannot be greater than the area of the surface in Planck units.
“horizon”
For each observer in a spacetime ( x0 = ct, x1 = x, x2 = y, x3 = z with signatures + - - - ),the surface beyond which he/she cannot see or receive signals from.
“information”
A measure of the organization of a signal. It is equal to the number of yes or no questions whose answers could be coded in the signal.
[L Smolin 2000 "Three roads to quantum gravity" London:Pheonix]
Another good source of learning more about entropy is from black hole physics in which the area theorem says for a (predictable) black hole satisfying Rab k^a k^b greater than or equal to zero, for all null k^a the surface area of a future horizon never decreases.
[Notation used: k^a means “k” with superscript a; “Rab” means R with suffixes a and b ]
Now the ordinary second law of thermodynamics states that the total entropy S never decreases with time. The area theorem is a rigorous theorem in differential geometry. The time asymmetry arises in the area theorem from the fact that we are dealing with a future horizon rather than a past horizon. The ordinary second law is not believed to be a rigorous law but rather one which holds with overwhelmingly high probability. The time asymmetry in the law arises from a choice of highly (improbable) initial state. There are ,however very few laws in physics which involve time asymmetric behaviour of of a quantity-allowing it to increase with time but not to decrease-so the striking mathematical analogy between these two laws cannot be dismissed a the classical level. The mass of the black hole, M plays the same role as the total energy of the thermodynamic system, E. Although the physical temperature of a classical black hole is zero, quantum mechanically the Hawking effect shows that K/2pi is the physical temperature of a black hole. But Hartle-Hawking relation gives[K=surface gravity]
(K /2pi)del[A/4] = (del[M]-w del[J] )
which on comparison with the ordinary first law
T del[S]= del[E]+Pdel[V]
Thus making the identifications M E and K/2pi T would strongly suggest that we could physically identify A/4 with S. Now A will tend to increase when the total entropy outside of black holes is decreased by dumping matter into a black hole. Similarly when A is decreased during the particlec creation process , thermal matter is created outside the black hole so Sm incresaes. Thus though Sm and A each can decrease individually, it is possible that the generalized entropy S’ defined by
S’ = Sm+1/4 A
never decreases. The conjecture that del[S’] > or = 0 in all processes was fiirst made by Bekenstein and is termed the generalized second law(GSL)
[ R M Wald 1994 "Quantum field theory in curved spacetime and black hole thermodynamics"Chicago:The ZUniversity Press;G t'Hooft 2009 "Dimentional reduction in quantum gravity" gr-qc/9310026 (Cellular automata is used as an example); J D Bekenstein2003 "information in the holographic universe"Live Jour/1190.htm]
( Notation used del [V]= delta V)
Corrections: The University Press not The ZUniversity Press. "Dimensional reduction .. not "Dimentional..
Sounds like a good discussion guys, unfortunately I'm too busy doing things in the real world to join in much these days. I'll check back later. Nice seeing you, Graeme!
Perhaps I need to repeat what I have already posted
"The Third Law makes our transition to quanum mechanical calculations possible. Taking |i> as a state with energy Ei and P as a quantum mechanical operator for a physical observer , then the expectation value or the average value of the observable is
= (1/Q) Sum(over |i>)[ exp(-Ei/kT)]
[Notation used: Integral (0 to a ) dx/x = log a ; Sum [ exp(-En/kT) ] = exp(-E1/kT) + exp(-E2/kT) + exp(-E3/kT) +…… +EN/kT ) ]
One may thus conclude that it is indeed a valid physical concept in physical chemistry, condensed state physics etc . It also features as an important ingredient of quantum cosmology and black hole physics"
Mathematical physicists have forwarded powerful logical arguments in favour of entropy as an entity in physics - perhaps I should say higher physics rather than O-level or A-level physics since time the days of Sir James Jeans and Sir Arthur Eddington. I believe modern mathematical physicists like Sir Roger Penrose ,Prof Stephen Hawking and Prof Ed Witten seem quite comfortable with entropy and Second Law of Themodynamics in their research work involving quantum theory. It is equally acceptible there!
Corrections:
Since the days of Sir James Jeans and Sir Arthur Eddington and I believe modern mathematical physicists like Sir Roger Penrose ,Prof Stephen Hawking and Prof Ed Witten seem quite comfortable with entropy and Second Law of Themodynamics in their research work involving quantum theory and (quantum) cosmology . It is equally acceptible there!
Considered as a conservation principle relating to energy the Second Law of Themodynamics is valid in all domains of physics may be not too apparent at the Quantum Mechanical level though!
To my way of thinking energy flow in the frame work of quantum mechanics is quite fascinating!In the Bardeen- Cooper - Schrieffer theory(not high Tc superconductivity) current consists of flow of electron pairs; the rather weak (quantum mechanical ) attraction between the so called Cooper pairs may be explained in terms of exchange of phonons or quanta of lattice vibrations between electron pairs. Creation and annihilation of phonons (or photons) ( as processes of energy exchange ) are quite the norm in many branches of physics including superconductivity. Also for the flow of superconductivity current without resistance the substance (superconductor) has to attain a very low temperature ie it has to be below a certain critical or transient temperature.
In this connection in 1935 an American experimentalist Shankland (Farmelo 2009 "The Strangest Man"London :Faber&Faber) seemed to have discovered some evidence that the law of conservation of energy did not hold in atomic phenomena. Dirac who was convinced that the law of conservation of energy should hold in atomic processes based on his quantum mechanical investigations wrote a paper speculating the consequences if Shanland' s results turned out to be true. Einstein and Schroedinger were also fascinated by Shankland's results which later could not be confirmed. Dirac was so let down by Shankland's experimental results that he adopted as his philosophy in physics that"It is more important to have beauty and consistency in one's theory than to have complete agreement with experiments"
In general , photons and phonons get created and destroyed in quantum processes but of course with superconductivity we need focus on phonons you are right ! Such processes are applicable both to fields and particles since deBrolgie's discovery of wave particle duality in 1924 and experimental work on electron diffraction by GP Thompson and Davisson and Germer Strictly speaking Dirac in 1927 and Wigner and Jordan soon afterwards discovered second quantization rules for bosons (particles like photons,phonons , mesons etc) and fermions(electrons ,protons, neutrons, baryons and quarks etc ) respectively! In formal terms one needs to use creation and annihilation operators to deal with BCS superconductivity Baredeen et al discovered normal or BCS superconductivity because they used a formalism involving creation and annihilation operators and Feynmann just missed it since he refused to use the formalism for a time. Much later Feynman also used quantum field theory in his work on condensed mstter physics and statistics. Feynman's work on quantum electrodynamics is of course well known. He used his own diagrammetic method (Feynman graphs) with a great deal of success! And only later and in his weak moments he used creation and annihilation operators !
Hello everyone,
Thank you all for your comments on this paper.
Because it is not very easy writing in english, I could not reply one by one, although I really want to reply every comment.
Thank you!
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