|American mathematician turned Lyndon LaRouche economist Jonathan Tennenbaum's hilarious 1993 attempt at refuting the laws of thermodynamics, per some type of anti-cybernetics negentropy argument.|
“There is thus no justification for the view, often glibly repeated, that the second law of thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the second law breaks down under any circumstances.”
To a good approximation, as soon as the second law was formulated, in circa 1860, and from there afterwards, there have been alleged or claimed proofs that the second law can be violated.
Any device, machine, or working entity that violates the second law is what is called perpetual motion of the second kind.
Opinions differ on the matter, but most agree that the second law of thermodynamics has never been violated (or shown to be false) and never will be violated; whereas a marginal number of others claim to find violations. Every experiment that has been conducted to disprove the validity of the second law or to show a violation of it has been unsuccessful.  The idea that violations could exist, however, remains a popular pastime; with over 100,000 Google search results, as of 2009, for the common search phrase "violation second law of thermodynamics". This popularity is likely related to the evolution/creationism debate. 
The earliest significant writings on the possibility that the second law might have loopholes seem to stem from Scottish physicist James Maxwell. As early as 1867, Maxwell had suggested to his associate Peter Tait that he should attempt to pick a hole in the second law of thermodynamics; a discussion that resulted in the now-famous Maxwell's demon.  Into the 1870s, Maxwell sought to prove that the second law may not be an absolute attribute of nature, but rather a result of incomplete and imperfect human perception; this effort may have been the result of his deep religious convictions, as a committed Evangelical, and a firm believer in the literal interpretation of the Bible, such as the story of Noah's flood, to which Maxwell would become very aroused if spoken of in disregard.  In 1878, Maxwell commented that: 
“The truth of the second law is therefore a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules, and that we never can get a hold of single molecule.”
A down fall in Maxwell's view is that single particle thermodynamics has been formulated; as well as sub-quantum thermodynamics, a term recently popularized by Gerhard Groessing (2008).
Maxwell, however, with his flawed demon argument, and noted entropy misinterpretation, for which he had to correct for in later editions of his Theory of Heat, may not have had a lucid understanding of the second law.
Poincaré recurrence theorem
See main: Poincaré recurrence theorem
In 1890, French mathematician Henri Poincaré, in his 1890 article “On the Three-body Problem and the Equations of Dynamics”, building on the previous work of French mathematician Simeon Poisson, stated that:
“It is proved that there are infinitely many ways of choosing the initial conditions such that the system will return infinitely many times as close as one wishes to its initial position … there are also an infinite number of solutions that do not have this property, but it is shown that these unstable solutions can be regarded as ‘exceptional’ and may be said to have zero probability.”
Six years later, in 1896, German mathematician Ernst Zermelo, an assistant to Max Planck, pointed out what he viewed as the apparent incompatibility between Poincaré’s recurrence theorem, Clausius’ second law, and Boltzmann’s H-theorem, in the sense that either the second law can be violated or connection to mechanical system cannot be made. Zermelo argued that the science of irreversible processes, thermodynamics, could not be reduced to mechanics, and reasoned that, for instance, German physicist Heinrich Hertz’s mechanical derivation of the second law must be impossible.
In 1921, English biologist James Johnstone gave a four page so-called "proof" using a terse bit of derivation and arguments about particles colliding in a body of gas to argue that "a system can, of itself, decrease its entropy" causing a reversal of the second law, and form a hot and cold body divide, starting from an originally uniform temperature body. The entire proof is barely readable in logic, but seems to have been done in attempts to explain the past state or history of the universe, in opposition to heat death theory, an issue that was prevalent prior to the initiation of big bang theory (1927-1949). At the end of his proof, Johnstone concludes "as such [our universe] is a permanent universe, self-sufficient, without beginning and without end." 
Prior to the 1940s, it was commonly asserted that life violates the second law in some way. To cite one example, in 1933 English physicist James Jeans reasoned that: 
“In fact it would seem reasonable to define life as being characterized by a capacity for evading this law. If probably cannot evade the laws of atomic physics, which are believed to apply as much to the atoms of a brain as to the atoms of a brick, but it seems able to evade this statistical laws of probability.”
In 1969, British developmental psychologist John Bowlby devoted the entire first chapter, entitled “Point of View”, of his three-volume famous Attachment series, in efforts to discredit Austrian Sigmund Freud in his use of physics terms, such as energy, entropy, force, pressure, or inertia, as in "principle of inertia", etc., in psychology, and on the topic of the second law states: 
To note although, in modern terms, one scoffs at this statement by Bowlby, many modern hard scientists have some some type of unwritten adherence to this.
The by far majority opinion, emerging after circa 1950, is that there are no violations of the second law. An example of this is found in the 1964 famous quote by Russian thermodynamicist Ivan Bazarov who states: 
“The second law of thermodynamics is, without a doubt, one of the most perfect laws in physics. Any reproducible violation of it, however small, would bring the discoverer great riches as well as a trip to Stockholm. The world’s energy problems would be solved at one stroke. It is not possible to find any other law (except, perhaps, for super selection rules such as charge conservation) for which a proposed violation would bring more skepticism than this one. Not even Maxwell’s laws of electricity or Newton’s law of gravitation are so sacrosanct, for each has measurable corrections coming from quantum effects or general relativity.”
Likewise, in 2008 American physical chemist Robert Mortimer stated his view on the matter as such: 
“No violation of either physical statement [Clausius or Kelvin statement] of the second law of thermodynamics has ever been observed in a properly done experiment … a machine that would violate the second law and turn heat completely into work in a cyclical process is called a perpetual motion machine of the second kind.”
A converse 1988 view comes from British astrophysicist Stephen Hawking, who also cited Newton's law, albeit in support of a possible violation: 
“The second law of thermodynamics has a different status than that of the other laws of science, such as Newton’s law of gravity, for example, because it does not always hold, just in the vast majority of cases.”Other
This particular quote, which stems from contrived ideal gas probability arguments (statistical mechanics), related particularly to a mixture of discussions on Maxwell's demon (1867), Loschmidt's paradox (1876), and the Poincaré recurrence theorem (1890), has become a common launching point for novice thermodynamics researchers who would like to argue that the second law can be violated, and that it particularly does so for the case of evolution. Indian chemical engineer DMR Sekhar, for instance, was stimulated to develop his 2007 genopsych theory based on this quote. 
Other supposed “mathematical proofs” can be found at a yearly rate claiming to have found violations of the second law. These violation claims are usually resolved by pointing out the areas of illogic used in the proof or argument. 
The 2002 article “Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales”, by a group of scientists from the Australian National University, involving a laser and the measure of entropy of tiny latex beads in water, according to American mathematician turned journalist Charles Seife, ‘caused a minor ruckus’. 
1. Hokikian, Jack. (2002). The Science of Disorder (section: Is Evolution a Miracle in Violation of the Second Law, pgs. 70-72). Los Feliz Publishing.
2. Rao, Y.V.C. (2004). An Introduction to Thermodynamics (pg. 213). Orient Blackswan.
3. Leff, Harvey S. and Rex, Andrew F. (2003). Maxwell’s Demon 2 (pg. 48). CRC Press.
4. Kragh, Helge. (2008). Entropic Creation: Religious Contexts of Thermodynamics and Cosmology (pgs. 53, 179). Ashgate Publishing, Ltd.
5. (a) Maxwell, James C. (1878). “Tait’s ‘Thermodynamics’ (I)”, (pgs. 257-59). Nature, Jan. 31.
(b) Maxwell, James C. (1878). “Tait’s ‘Thermodynamics’ (II)”, (pgs. 278-81). Nature, Feb. 07.
6. Bazarov, Ivan P. (1964). Thermodynamics. Pergamon.
7. Mortimer, Robert G. (2008). Physical Chemistry (pg. 106). Academic Press.
8. Hawking, Stephen. (1988). A Brief History of Time. New York: Bantam Books.
9. Email communicate from DMR Sekhar to Libb Thims in January 2009.
10. Gyftopoulos, Elias P. (2002). “Comments on Violations of the Second Law”, arxiv.org.
11. Jeans, James. (1933). The New Background of Science (pg. 280). CUP Archive.
12. Bowlby, John (1969). Attachment and Loss: Vol I, 2nd Ed. (pgs. 20). Basic Books.
13. Pippard, A.B. (1957). Elements of Chemical Thermodynamics for Advanced Students of Physics (pg. 100). Cambridge University Press.
14. Johnstone, James. (1921). The Mechanism of Life in Relation to Modern Physical Theory (pgs. 192-203). New York: Longmans, Green & Co.
15. (a) Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J. and Evans, D.J. (2002). “Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales” (abstract), Physical Review Letters 89.
(c) Nieuwenhuizen, Theo M. and Allahverdyan, Armen E. (2002). “Comment on: “Experimental Violations of the Second Law of Thermodynamics for Small Systems and Short Timescales” (abs), ArXiv.org.
(b) Seife, Charles. (2007). Decoding the Universe: How the New Science of Information is Explaining Everything in the Cosmos, from Our Brains to Black Holes (pgs. 72-79). Penguin Books.
● Gross, Dieter H.E. (2001). Microcanonical Thermodynamics (secion: 2.4.1: Convex entropy – Violation of the Second Law?, pgs. 31-32). World Scientific.
● Whitehouse, David. (2002). “Beads of Doubt”, 18 July, BBC News.
● Capek, V. and Frege, O. (2002). “Violation of the 2nd Law of Thermodynamics in the Quantum Microworld” (abstract), Czechoslovak Journal of Physics, Vol. 52, No. 5, May.