Second law of thermodynamics

The second law of thermodynamics is consider to be one of the “strongest” laws of Nature.

The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. (.)

Right away by reading the above definition you understand that the second law of thermodynamics has to do with statistics. In schools we learn that the 2nd law of thermodynamics is the expression of the axiom of conservation of energy, and that is the reason that it is so “strong”. What they don’t teach us is that conservation of energy is a statistical phenomenon that we experience in the macroscopic world, despite that this was demonstrated 150 years ago by James Clerk Maxwell with his famous demon thought experiment;

second law of thermodynamics.. if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics….

One better understanding of the second law of thermodynamics is through entropy¹;

The second law of thermodynamics states that the total entropy of an isolated system must increase. Since the demon and the gas are interacting, we must consider the total entropy of the gas and the demon combined. The expenditure of energy by the demon will cause an increase in the entropy of the demon, which will be larger than the lowering of the entropy of the gas. (.)

The demon will consume energy and increase the energy of the whole system, so the second law of thermodynamics is safe again. But it really depends on what this demon is, what about if the demon does not increase the entropy of the system by operating in thermodynamically reversible² way?

In 1960, Rolf Landauer suggested these “reversible” measurements could be used to sort the molecules, violating the Second Law. (.)

The second law of thermodynamics is not safe again, and in order to defend it we have to understand what entropy really means;

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.(.)

Taking in account the above definition of entropy, then the arguments in favor of the second law of thermodynamics exchange energy with information;

In 1982, Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. (Many people run into this problem of running out of storage space on their own computers but fortunately there is a simple solution – deleting some of the unnecessary data. A Maxwellian demon could do the same thing, deleting earlier data. But memory erasure is by definition an irreversible process. Once you’ve deleted the data on a piece of memory, resetting all the bits to 0, it is impossible to reconstruct the original data from this string of 0s. This irreversible process increases entropy by k ln 2 per bit. Bennett realised that one bit of storage was needed for each Szilard cycle. The entropy increase when these bits are erased offsets the entropy decrease effected by the demon.(.)

Despite that even this argument does not “save” the second law of thermodynamics ³ it achieves an important transformation; energy is exchanged with information, and the quest of defending the second law can be understood in terms of information exchange.

Finally 150 years later scientists and engineers managed to create the first implementation of Maxwell’s demon; Physicists Convert Information Into Energy For the moment they don’t seem to care about the quest of defending the second law of thermodynamics, they are excited that they have a principle for creating a nano-scale engine that converts information to energy.


¹Entropy is a macroscopic property of a thermodynamic system that is a measure of the microscopic disorder within the system. It is defined by the second law of thermodynamics. Thermodynamic systems are made up of microscopic objects, e.g., atoms or molecules, which carry energy. According to the second law of thermodynamics, the thermodynamic entropy is a measure of the amount of energy which does no work during energy conversions.

²In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be “reversed” by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic equilibrium throughout the entire process. Since it would take an infinite amount of time for the reversible process to finish, perfectly reversible processes are impossible. However, if the system undergoing the changes responds much faster than the applied change, the deviation from reversibility may be negligible. In a reversible cycle, the system and its surroundings will be exactly the same after each cycle.

³ John Earman and John Norton have argued that Szilárd and Landauer’s explanations of Maxwell’s Demon begin by assuming that the second law of thermodynamics cannot be violated, thus rendering their proofs that Maxwell’s Demon cannot violate the Second Law circular. (.)


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