[7] For a long time, exact results in thermodynamics were only possible in linear systems capable of reaching equilibrium, leaving other questions like the Loschmidt paradox unsolved.
During the last few decades fresh approaches have revealed general laws applicable to non-equilibrium system which are described by nonlinear equations, pushing the range of exact thermodynamic statements beyond the realm of traditional linear solutions.
[8] The mathematical resolution to Loschmidt's paradox is called the (steady state) fluctuation theorem (FT), which is a generalisation of the second law of thermodynamics.
The FT was first put forward by Evans et al. (1993)[9] and much of the work done in developing and extending the theorem was accomplished by theoreticians and mathematicians interested in nonequilibrium statistical mechanics.
[b][7] The first observation and experimental proof of Evan's fluctuation theorem (FT) was performed by Wang et al. (2002)[10] Seifert writes:[8] This is shown to be a special case of a more general relation.
Quantum coherence can be used in effect to play the role of Maxwell's demon[16] though the broader information theory based interpretation of the second law of thermodynamics is not violated.
Experiments have suggested that the Jarzynski equality does not hold in some cases due to the presence of non-Boltzmann statistics in active baths.
For example, biomolecules within cells are coupled with an active bath due to the presence of molecular motors within the cytoplasm, which leads to striking and largely not yet understood phenomena such as the emergence of anomalous diffusion (Barkai et al., 2012).