non-equilibrium processes, as is so for macroscopic descriptions, a general definition of entropy for microscopic statistical mechanical accounts is also lacking. Technical note: For the reasons discussed in the article differential entropy, the simple definition of Shannon entropy ceases to be directly applicable for random variables with continuous probability distribution functions. Instead the appropriate quantity to maximize is the "relative information entropy," Hc is the negative of the Kullback–Leibler divergence, or discrimination information, of m(x) from p(x), where m(x) is a prior invariant measure for the variable(s). The relative entropy Hc is always less than zero, and can be thought of as (the negative of) the number of bits of uncertainty lost by fixing on p(x) rather than m(x). Unlike the Shannon entropy, the relative entropy Hc has the advantage of remaining finite and well-defined for continuous x, and invariant under 1-to-1 coordinate transformations. The two expressions coincide for discrete probability distributions, if one can make the assumption that m(xi) is uniform - i.e. the principle of equal a-priori probability, which underlies statistical thermodynamics. Philosophical implications Adherents to the MaxEnt viewpoint take a clear position on some of the conceptual/philosophical questions in thermodynamics. This position is sketched below. The nature of the probabilities in statistical mechanics Jaynes (1985, 2003, et passim) discussed the concept of probability. 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). The probabilities are objective in the sense that, given these inputs, a uniquely defined probability distribution will result, the same for every rational investigator, independent of the subjectivity or arbitrary opinion of particular persons. The probabilities are epistemic in the sense that they are defined in terms of specified data and derived from those data by definite and objective rules of inference, the same for every rational investigator. Here the word epistemic, which refers to objective and impersonal scientific knowledge, the same for every rational investigator, is used in the sense that contrasts it with opiniative, which refers to the subjective or arbitrary beliefs of particular persons; this contrast was used by Plato and Aristotle, and stands reliable today. Jaynes also used the word 'subjective' in this context because others have