More specifically, MaxEnt applies inference techniques rooted in Shannon information theory, Bayesian probability, and the principle of maximum entropy.
These techniques are relevant to any situation requiring prediction from incomplete or insufficient data (e.g., image reconstruction, signal processing, spectral analysis, and inverse problems).
The given data state "testable information"[3][4] about the probability distribution, for example particular expectation values, but are not in themselves sufficient to uniquely determine it.
The approach also creates a theoretical framework for the study of some very special cases of far-from-equilibrium scenarios, making the derivation of the entropy production fluctuation theorem straightforward.
For non-equilibrium processes, as is so for macroscopic descriptions, a general definition of entropy for microscopic statistical mechanical accounts is also lacking.
According to the MaxEnt viewpoint, the probabilities in statistical mechanics are determined jointly by two factors: by respectively specified particular models for the underlying state space (e.g. Liouvillian phase space); and by respectively specified particular partial descriptions of the system (the macroscopic description of the system used to constrain the MaxEnt probability assignment).
He accepted that in a sense, a state of knowledge has a subjective aspect, simply because it refers to thought, which is a mental process.
But he emphasized that the principle of maximum entropy refers only to thought which is rational and objective, independent of the personality of the thinker.
One writer even goes so far as to label Jaynes' approach as "ultrasubjectivist",[9] and to mention "the panic that the term subjectivism created amongst physicists".
The fitness of the probabilities depends on whether the constraints of the specified macroscopic model are a sufficiently accurate and/or complete description of the system to capture all of the experimentally reproducible behavior.
So long-term time averages and the ergodic hypothesis, despite the intense interest in them in the first part of the twentieth century, strictly speaking are not relevant to the probability assignment for the state one might find the system in.
Failure to accurately predict them is a good indicator that relevant macroscopically determinable physics may be missing from the model.
According to Liouville's theorem for Hamiltonian dynamics, the hyper-volume of a cloud of points in phase space remains constant as the system evolves.
Instead of being easily summarizable in the macroscopic description of the system, it increasingly relates to very subtle correlations between the positions and momenta of individual molecules.
Equivalently, it means that the probability distribution for the whole system, in 6N-dimensional phase space, becomes increasingly irregular, spreading out into long thin fingers rather than the initial tightly defined volume of possibilities.
Classical thermodynamics is built on the assumption that entropy is a state function of the macroscopic variables—i.e., that none of the history of the system matters, so that it can all be ignored.
The extended, wispy, evolved probability distribution, which still has the initial Shannon entropy STh(1), should reproduce the expectation values of the observed macroscopic variables at time t2.
At the level of the 6N-dimensional probability distribution, this result represents coarse graining—i.e., information loss by smoothing out very fine-scale detail.
It is also sometimes suggested that quantum measurement, especially in the decoherence interpretation, may give an apparently unexpected reduction in entropy per this argument, as it appears to involve macroscopic information becoming available which was previously inaccessible.
Quite possibly, it arises as a reflection of the evident time-asymmetric evolution of the universe on a cosmological scale (see arrow of time).
The Maximum Entropy thermodynamics has some important opposition, in part because of the relative paucity of published results from the MaxEnt school, especially with regard to new testable predictions far-from-equilibrium.
Balescu states that Jaynes' and coworkers theory is based on a non-transitive evolution law that produces ambiguous results.
Classical physical definitions of entropy do not cover this case, especially when the fluxes are large enough to destroy local thermodynamic equilibrium.
In other words, for entropy for non-equilibrium systems in general, the definition will need at least to involve specification of the process including non-zero fluxes, beyond the classical static thermodynamic state variables.