Dear Gokaran,

You have probably consulted the very first paper of Jarzinsky, but even in his second paper on his famous identity, he deals with master equations (as well as Crooks, as far as I can tell). These are already derivations with use some element of stochasticity, although underlying detailed balance in absence of driving is assumed. Kurchan derived later the same work relations in the context of stochastic processes described by Langevin equations, or equivalently, Fokker-Planck equations. And the field has advanced a lot since then. For instance, one has the seminal work of Hatano an Sasa dealing with the thermodynamics of Langevin systems with broken detailed balance (nonequilibrium steady states). It is important to mention two things.First, that the fact that a process is described by Fokker-Planck equations doesn't mean that its dynamics is irreversible. It's the detailed balance condition who accounts for irreversibility in a stochastic system. Second, the question, as usual in physics, is not if a given theoretical framework is an idealization (every theoretical framework is) but to what extend such idealization is useful to describe, and most importantly, make predictions about the real world.

Cordially,

Reinaldo.

Gokaran Shukla

From a perspective of a pure mathematician you are right: no thermodynamic process is really reversible, and closed/isolated systems do not exist, strictly speaking.

However a good physicist is aware that reversible thermodynamic processes and closed/isolated systems are often very good approximations of the reality. Therefore there is no chance that research in the last 20 years went in the wrong direction globally; however surely some researchers could have gone in the wrong direction.

No thermodynamic process is really reversible, a thermodynamic process requires a driving force, a gradient of thermodynamic force, this gradient will be dissipated in an irreversible process, and cannot be fully recovered without compensation, reversible process assumes that a process goes infinitely slow, and the thermodynamic gradient approximates zero, it is only a limit case in the theory.

Closed/isolated systems are only a theoretical approach, strictly speaking, “closed/isolated” is not an essential requirement, it only denotes that there are no some energy/matter exchange processes between a system and its surroundings.

Thermodynamics does not seem like a perfect theory in the usual sense because it is a black-box theory apart from some parts of chemical thermodynamics, which describes that a black-box exchange energy/matter with its surroundings but can hardly describe internal change in the box(system), non-equilibrium thermodynamics only divide a big black-box（system） into some small black-boxes（locals）but not open the black-box, so it is the sum of small black-boxes theory.

Dear Reinaldo,

I have read Both Zarzynski paper where he derives identity using master equation. I have also read Crook fluctuation theorem. Unfortunately all are wrong for any real thermodybsmical system . The point is that no heat bath is available in any real thermodynamics system which supply required dissipative energy at each time step and mantained phase space volume. Crooks and Zarzynski relation are only valid for isolated system. Unfortunately , no real isolated and closed system possible. For more understanding, read ny comment on Zarzynski equality which available on my timeline.

Dear Andrea,

If one use approximation then one should keep in mind that final answer will be approximated one, and then one should not challenge the second law of thermodynamics.

Dear Gokaran,

I must honestly say that I'm not prepared to abandon well established science so easily, at least not for the moment. When I read your argument, it's not Jarzynski and Crooks relations whiat you are fundamentally questioning. You are arguing that they are invalid because the constructions they rely upon (ideal thermostat, closed systems, etc) do not exist in nature. It is then the whole thermodynamics and statistical mechanics as we know it today what you're uncomfortable with, in my opinion. Basically, there are not new constructions in the derivation of the work theorems, these constructions you criticize were already there for a long time before. Even the second law of thermodynamics, when enunciated in terms of entropy, relies on isolated systems. So I'm not quite sure to fully understand your argument.

With best regards,

Reinaldo

Dear Reinaldo,

Zarzynsky and Crooks theorems are the direct threat to the second law of thermodynamics. Second law of thermodynamics is valid for every system (open,close, isolated) at any time and length scale. (please look up my project, the second law of thermodynamics and its implication). May be you can read my paper, Flaw in Crooks fluctuation theorems or Flaw in Maxwell demon paradox. I have discussed the second law of thermodynamics in great details. Nothing can evolves in any directional process without paying to the surrounding. This is a fact. One have to accept it. There is NO other choice left. Zarzynski and Crooks are claiming that they can predict change in Gibbs/Helmholtz free energy in any system using any irreversible process which is very very absurd. I have read some work of R. Kubo on the non equilibrium thermodynamics. I must say that he have tried his best. Unfortunately we don't have any non equilibrium thermodynamics relation which is correct in our hand. This is a harsh reality. This field need to be developed after exposing Zarzynski and Crooks. Statistical thermodynamics are only valid for ideal system (either perfectly closed or perfectly isolated). Unfortunately, perfectly close and isolated system are impossible in real life. Reason is very pure that space is perfectly continuous and connected. It will not allow to make perfect close and isolated system. For example, you will NEVER get any material which have perfect ZERO diffusion coefficient at any non-zero temperature and pressure. Perfectly you will NEVER able to isolate heat from surrounding. You can only minimize the thermal diffusion coefficient. But this coefficient will never be perfect absolute ZERO. This is a fact and this is all happening due to the surrounding intervention which is nothing but the second law of thermodynamics itself. We have no choice except abandon Zarzynski and Crooks relations. Both relation are only valid for ideal reversible system. Nothing is reversible in real system. In real system any directional process evolves under the presence of finite gradient in every time step. Finite gradient will turn every directional process irreversible. For example, time can not flow back, you can not get you childhood back. This all happening because of the second law of thermodynamics. I am surprised that Zarzybski and Crooks played successfully a greatest BLUFF in the history of science without any resistance from the scientific community. They must need to be exposed. Science will never flourish with the lies and Deceit.

Dear Gokaran,

"Jarzynsky and Crooks theorems are the direct threat to the second law of thermodynamics."

This is a strong, I would dare to even say emotional statement, but I don't see how. I'm being honest, I don't see how they are threatening the second law. The second law of thermodynamics is a statistical law, and it was understood like that even by Boltzmann. There's no surprise that in individual realizations of stochatic processes with just a few degrees of freedom, things are different.

"Second law of thermodynamics is valid for every system (open,close, isolated) at any time and length scale."

What I said was that enunciation of the second law in terms of entropy, includes considering an isolated system, i.e., there's no process in an isolated system for which entropy decreases. In a system able to exchange energy and matter with iits surroundings, this does not hold true anymore, and this is why there're living things, for instance. So, entropy decresing in an open system does not contradict at all the second law.

"Nothing can evolves in any directional process without paying to the surrounding. This is a fact. One have to accept it. "

If you think that the work theorems contradict this, then you should probably revise the derivations again. Besides Jarzynski and Crooks, have you also read the paper by Jorge Kurchan I mentioned?

"Jarzynski and Crooks are claiming that they can predict change in Gibbs/Helmholtz free energy in any system using any irreversible process which is very very absurd."

In my opinion, this comment is again, emotional. Why don't you back it up? The mathematics behind their derivations is straightforward. I would understand you better if you point out where is the flaw in their derivation. Which steps are incorrect?

"This field need to be developed after exposing Zarzynski and Crooks. Statistical thermodynamics are only valid for ideal system (either perfectly closed or perfectly isolated)"

I don't know what do you mean by "perfectly". Closed and isolated systems are constructions that, again, exist since a very long time ago. If what you mean is that there isn't any natural system that corresponds perfectly to such idealizations, I can say that yes, that's true. Nevertheless these are very good approximations in a considerably large number of cases. I repeat myself and say that ALL constructions of physics are ideal. Nature is what it is, not what our models say. But we do a pretty good job not only at describing known things, but also at predicting new phenomena using such idealized constructions.

" For example, time can not flow back, you can not get you childhood back. This all happening because of the second law of thermodynamics. I am surprised that Zarzybski and Crooks played successfully a greatest BLUFF in the history of science without any resistance from the scientific community. "

Because most people don't see in these results what you claim they're saying.If you find that these are consecuences of those results and we are all blind, then you should put together a convincing, mathematicaly strong and physically sound argument. Could you for instance show that Jarzynski equality means that time flows back? And what do we know about time, by the way? Are you relying in your human senses to say that the arrow of time is equaly valid at the microscale? The very same senses that can't grasp time dilation in relativity? What is time in a chaotic space of a few degrees of freedom? Would you actually have the same "feeling" of time if you where just a molecule in the air?

Best wishes,

Reinaldo.

Dear Reinaldo,

“Even the second law of thermodynamics, when enunciated in terms of entropy, relies on isolated systems. “

This is incorrect, for an open system,

dS=diS+deS

where, diS is the internal entropy production, deS is the entropy flux, the second law

diS≥0

Best regards，

Tang Suye

Dear Tang,

Read my response above to Gokaran. There's nothing incorrect in what i said with words. I never said that the second law is violated if the system is open. I said that enunciation of the law is as simple as "In an isolated system, spontaneous process cannot decrease the entropy of the system", that's all. What you wrote is totally compatible with what I'm saying, because entropy production accounts for the entropy change in the system+environment, which is, by construction, isolated.

Best wishes,

Reinaldo

Dear Reinaldo,

Zarzybsky and Crook theorems are threat to the second law of thermodynamics for following reason:

(1) The second law of thermodynamics says that if any directional process evolves in nature, then it MUST pay to the surrounding at any non-zero temperature and pressure. A directional Process can not move forward/backward if it does not pay to surrounding. The direct consequence of this basic fact is that No engine can have 100% efficiency. Carnot efficiency (maximum efficiency which will always less than 100%) is the direct consequence of this law.

(2) Every directional process is an Ir-reversible process. Ir-reversibility decreases/increases energy of the system and increases entropy for the system+surrounding. Zarzynski and Crooks uses reversible equation, phase space volume continuity equation and derives non-sense relation. .

(3) Every collision in nature is inelastic collision. The degree of in-elasticity (coefficient of restitution) vary from process to process and collision to collision. In other words, No collision in nature are the perfect elastic collision. The consequence of this thermodynamical fact is that, the origin of friction force. Friction force will always appear in any type of collision. If friction force appear then Volume of the phase-space will NOT conserve. You will not able to use Liouville equation of motion in such dissipative system. Now you can think that what will happens to your Stochastic process in real system. Whether your Stochastic process applicable to any real thermodynamical system or not?

Zarzynski uses Liouville equation of motion. He have used detail balance in phase space and concluded that phase space volume is conserved. He can not use detail balance until or unless ALL dissipative forces which are highly non-linear in nature are known completely. Also, he can not use continuity equation in dissipative system. In dissipative system phase-space volume shrink. Take for example simple pendulum in resistive media. Simple pendulum phase-space volume will shrink in every-time and finally it will become zero. He also uses reversibility concept in the directional process. He is not aware the basic fact that directional process evolves under the presence of finite chemical/magnetic/ electric/ gravitational potential energy gradient. Any sort of gradient will make whole process Ir-reversible. Also, entropy always increases in irreversible process in every time steps. There is no time step in which entropy has decreases. If entropy has not decreases in any time step then how can Crooks uses probabilistic definition of entropy and claims that in some time interval process entropy has decreases?

Also, Zarzynski and Crooks have no idea that in any ir-reversible process, work done on/by the system is strongly dependent on the speed, surrounding configuration, exponent of gas,..... Work done process will be highly non-linear.. No definite relation can be obtain in such process......Work done will always be STRICTLY GREATER than the change in Gibbs/Helmholtz free energy of the system. Both have no physical feeling that STRICTLY GREATER THAN(>) is not the same as EQUAL TO(=). (Read my paper, Flaw in Crooks fluctuation theorems, and comment on Zarzynski equality. Both paper are available on my time-line)

Also, perfect closed means that in perfect closed system mass can not be exchanged with the surrounding. Show me one material (you will use material to make wall of your system) which has perfect ZERO mass diffusion coefficient? This mass diffusion coefficient can be very very small number but this value will never become zero. If Mass diffusion coefficent is non-zero then there will be mass diffusion flux (Fics Law) across the wall in the system. No matter how small this number is but this number will be finite non-zero . So, perfect close system is NOT possible. The similar argument can be given for an Isolated system as well. Energy will flow across the wall. You will never able to make this energy flux zero. You can only minimize thermal diffusion coefficient value of any material but this value will never become perfect zero. To stop the energy flow in the system you need perfect thermal diffusion coefficient which MUST have perfect zero value. This happens because space which is present everywhere is continuous and perfectly connected. material space is perfectly connected to the external worlds. If any kind of gradient exist between system and surrounding (For example, concentration gradient, temperature gradient, potential energy gradient,pressure gradient, then as time progress, nature will make sure that gradient will decreases with time and it will disappear finally (thermodynamics equilibrium) . This happens due to the second law of thermodynamics.

As for as your time definition is concern, let me ask few question first.:

Can you please explain why every mass in nature rotates about it axis? Be is smallest mass like Proton, neutron, electron or massive mass like Earth and Sun? And why they rotates counter-clockwise?

Dear Gokaran,

I don't comment JE. As I said above, thermodynamics is a black-box theory, if you open this box, many questions will become simple and clear, below are some of my view.

a) The internal energy or thermodynamic energy can be and should be classified into the two kinds, one is heat energy (with some quality loss), the entropy of heat energy is larger than zero, another one is free energy, the entropy of the free energy is equal to zero（no quality loss）.

b) Work W itself is the free energy transport (process), or free energy flux, in an irreversible process, work W partly be converted into heat energy without compensation, so we have F < W.

c) The equal a priori probability postulate only hold in the case when thermal motion stronger than interaction，whereas, thermodynamics does not need to consider this postulate, so the valid range of statistical mechanics is less than thermodynamics, which is only the part of the micro explanation of thermal motion in thermodynamics, but not all. In many cases, the equal a priori probability postulate is inapplicable, such as crystallization, solidification, phase transitions, which is also completely incompatible with many concepts, such as genes，self-organize, etc,

Best regards，

Dear Tang

If you accept F

Dear Gokaran

Yes, I never accept JE.

Gokaran Shukla

"Dear Andrea, If one use approximation then one should keep in mind that final answer will be approximated one, and then one should not challenge the second law of thermodynamics."

I agree with Reinaldo Garcia-Garcia: noone challenged it. I think this discussion went into the realm of philosophy. I would remind you that Physics is the approximation of reality.

Dwar Andrea,

There are thousands of paper which challenge second law if thermodynamics. Most paper uses either Zarzynski, or Crooks theorems, or Maxwell demon paradox at nano scale level. Some of even extracting useful work even in thermodynamics equilibrium using Maxwell demons. These paper has been published in PRL, NATURE, SCIENCE journals. So you are not quite right that no one is challenging. Also, I don't agree with you that physics deal approximated reality of nature. Quantum mechanics is very very successful theory. I can tell you without ant doubt that QM, DFT, Max planck black body radiation theory are perfectly correct.

The Crooks fluctuation theorem (CFT) seems to confuse time-reversal with mirror-image system.

A reversal symmetry means that the mirror-image process of a mirror-image system be allowed to happen according to the laws of physics, but does not denote that the process of a system can be reversed along the reverse trajectory or change the law of physics, such as velocity inversion in micro-dynamics.

For a system {mi, vi}, by {vi}→{-vi}, we get a mirror-image system {mi,-vi} , which is another system, and the mirror-image process of the mirror-image system {mi,-vi} be allowed to happen due to velocity-reversal symmetry, this is another process, it does not mean that the process of the system {mi, vi} can be reversed along the time reversal path.

Where, {mi,vi} and {mi,-vi} are the two systems, they are mirror-image systems for each other.

In irreversible thermodynamics, time-reversal cannot reverse the direction of thermodynamic gradient, so a mirror-image process cannot be allowed to happen according to the second law, for Fourier equation

[∂T/∂t]=κ[∂2T/∂x2],

since the coefficient of heat conduction κ is positive definite, we cannot change the plus sign of κ into minus, so for time-reversal, we get different equation

[∂T/∂t]=-κ[∂2T/∂x2].

It means that Fourier equation has been changed.

In my view, the joint probability of the reverse trajectory in CFT makes no sense.

Dear Tang,

You are in very right direction. Crooks theorems and Zarzynski equality are very very wrong. Directional Thermodynamics driven by gradient and make whole process ir reversible.

Dear Tang, dear Gokaran,

NO, you are clearly conflating time-reversal operation with something else. The example above of the diffusion equation is what definitely convinces me of this fact. If you have a stochastic process and you compute the path probability it prescribes for trajectories (which has nothing to do with Jarzynski and Crooks, this is standard stochastic calculus) you find that for ANY trajectory, the time-reversed trajectory (microscopic trajectory of the stochastic process) has a well defined and non-zero probability (this in not surprising, a the time-reversed trajectory of a given one, is also one of the trajectories contributing to the probability weight). This is why I was recommending you to do the calculations yourself, and pointing out to that paper of Kurchan where he deals with Langevin processes. Of course, when the size of the system increases, some trajectories (typically called 'atypical') will have a prohibitely small probability weight, as is visible from a large deviation principle. This is second law naturally emerging at the macroscale. The second law IS a statistical law. Which is why in small systems, entropy production rate is strictly positive in average. But only in average. In the thermodynamic limit, large deviation principle guarantees it to be positive for all realizations.

Best,

Reinaldo.

Dear Reinaldo,

In Langevin equation you have third term which is always positive. Do you know what impact it has on the phase space volume evolution? And why this term is positive? From where you are getting energy to maintain the probability distribution function? If all collision in nature are perfectly inelastic (read Kubo paper where he cited Einstein for the origin of friction force. Paper is attached to this post) then how will you maintain the total energy of the system? If total energy does not maintain then phase space volume will shrink. Second, are you agree with the basic fact that every directional thermodynamical process evolves under the presence of finite chemical potential energy gradient at each time step (including microscopic level)? Have you notice that presence of finite gradient in any system will Guarantee that you MUST PAY to the surrounding?. In other words, efficiency of the process will be less than one ?

Third, The second law of thermodynamics is NOT the statistical average law. Statics has been used to understand it. Using any method depends on the human capability and the result in hand. It does not guarantee that use process can dictates to the nature and its physical reality. You must use Grand canonical ensemble if you really want to understand the second law of thermodynamics. You can not use canonical or micro canonical ensemble to understand any physical process in real life.

Fourth, you need to accept that Crooks fluctuation theorems and Zarzynski equality are absurd if you use it in any real directional thermodynamical process. Because every directional thermodynamical process are irreversible process in nature. Ir reversibility is the essence of life. The existence of one way time advances, increasing entropy, existence of magnetism and existence of permanent polarization in certain solids are living testimony of Ir-reversibility.

Fifth, if you are using Zarzybski and Crooks fluctuation theorem in you research then you are fooling yourself and wasting your time. You will never able to design anything which will follows Zarzynski and Crooks fluctuation, because you can NEVER ABLE to fool the Nature. Nature follows the second law of thermodynamics absolutely. I recommend you to read my paper " impossibility of the continuous persistent current in a superconductor".

Dear Reinaldo,

Every collision is an in-elastic collision in absolute sense. Using Stochastic process in any system is nothing more than a sophisticated bluff towards general audience . You can fool few people some time but not all the time. You can NOT DICTATES the nature and change the physical reality that every collision is NOT an inelastic collision in absolute sense. You just name one real physical process where collision is perfect elastic? Other than that, the origin of friction force is due to pure quantum mechanical effect. You have to overwrite QM if you want to use stochastic process in any real thermodynamic process and use elastic collision which is of-course absurd ..Unfortunately, no one has ability to overthrow QM and dictates Nature

Dear Reinaldo,

I think you had not understood what I said in the previous comment. The two equations means that for an irreversible process，we cannot do time-reversal operation, which will lead to that heat transport from low temperature to high temperature. In general, time-reversal operation cannot be done for an equation/formula which related to the second law, so, the time-reversed trajectory makes no sense for an irreversible process due to which is a violation of the basic law.

Attention, please，here we discuss the second law, not an equation of motion.

A pretty girl marries a handsome boy, then they have a baby, this an irreversible process, and conforms to the second law, I'm very interested, how do you describe this story by stochastic process, by fluctuation, and what is the joint probability of the reverse trajectory in this story?

My question is the theoretical premise in CFT, not the calculations! If the theoretical premise is wrong, the calculations make no sense.

Best regards，

Tang Suye