Conditional maximum entropy and superstatistics

Abstract

Superstatistics describes nonequilibrium steady states as superpositions of canonical ensembles with a probability distribution of temperatures. Rather than assume a certain distribution of temperature, recently [2020 J. Phys. A: Math. Theor. 53 045004] we have discussed general conditions under which a system in contact with a finite environment can be described by superstatistics together with a physically interpretable, microscopic definition of temperature. In this work, we present a new interpretation of this result in terms of the standard maximum entropy principle using conditional expectation constraints, and provide an example model where this framework can be tested.

Conditional Entropic Approach to Nonequilibrium Complex Systems with Weak Fluctuation Correlation

“…A point to be emphasized here is that in contrast to the works [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ] mentioned earlier, the quantity to be maximized is the conditional entropy associated with the slowly fluctuating variable, recalling the dominant role of in Equation (2).…”

“…In recent years, various discussions have been developed about using the maximum entropy principle [ 2 ] for treating nonequilibrium complex systems organized hierarchically by different dynamics on largely separated time scales, e.g., as in Refs. [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ]. For the joint distributions describing these systems, there often exists a situation that the distribution to be examined is the marginal one while the conditional distribution is well understood, which is somewhat in contrast to the situation we consider here.…”

Conditional entropy and weak fluctuation correlation in nonequilibrium complex systems

“…The maximum entropy principle [2] has been used as the crux for treating nonequilibrium complex systems with a hierarchical structure of different dynamics on different time scales, as in recent works, e.g., in Refs. [3][4][5][6][7][8][9][10], where the joint entropy associated with the fast and slow dynamics or the marginal entropy concerning the slow dynamics is maximized. For the joint entropy, the marginal distribution is of central importance while the conditional distribution is well understood by local equilibria, there.…”

The $q$-canonical ensemble as a consequence of Bayesian superstatistics

“…Regarding this question, the issue of whether a generalization of the Boltzmann-Gibbs entropy, such as the one proposed by Tsallis [1,2] is required to explain such distributions is still an open question, given the rise of alternative proposals such as Superstatistics [3,4] among others [5,6]. Superstatistics in particular is strongly founded on the rules of probability theory while still being compatible with Jaynes' original maximum entropy principle [7] and is therefore an appealing choice of framework. Moreover, superstatistics is especially suited to the language of Bayesian probability, as has been shown in several different works [8][9][10][11][12][13].…”