Philip Ball in Quanta:
In all of physical law, there’s arguably no principle more sacrosanct than the second law of thermodynamics — the notion that entropy, a measure of disorder, will always stay the same or increase. “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations,” wrote the British astrophysicist Arthur Eddington in his 1928 book The Nature of the Physical World. “If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” No violation of this law has ever been observed, nor is any expected.
But something about the second law troubles physicists. Some are not convinced that we understand it properly or that its foundations are firm. Although it’s called a law, it’s usually regarded as merely probabilistic: It stipulates that the outcome of any process will be the most probable one (which effectively means the outcome is inevitable given the numbers involved).
Yet physicists don’t just want descriptions of what will probably happen. “We like laws of physics to be exact,” said the physicist Chiara Marletto of the University of Oxford. Can the second law be tightened up into more than just a statement of likelihoods?
A number of independent groups appear to have done just that.
More here.