The basis of all of our development up to this point has been the cluster ensemble, a discrete ensemble that generates every possible distribution of integers i with fixed zeroth and first order moments. Thermodynamics arises naturally in this ensemble when M and N become very large. In this chapter we will reformulate the theory on a mathematical basis that is more abstract and also more general. The key idea is as follows. If we obtain a sample from a given distribution h 0 , the distribution of the sample may be, in principle, any distribution h that is defined in the same domain. This sampling process defines a phase space of distributions h generated by sampling distribution h 0 . We will introduce a sampling bias via a selection functional W to define a probability measure on this space and obtain its most probable distribution. When the generating distribution h 0 is chosen to be exponential, the most probable distribution obeys thermodynamics. Along the way we will make contact with Information Theory, Bayesian Inference, and of course Statistical Mechanics.
CITATION STYLE
Matsoukas, T. (2018). Generalized Thermodynamics. In Understanding Complex Systems (pp. 197–239). Springer Verlag. https://doi.org/10.1007/978-3-030-04149-6_7
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