Descriptive thermodynamics

Sampling and statistical physics via symmetry

“…methods, and the characteristic timescale may be dictated either by the data itself or by the collection interval. In many ways this "descriptive thermodynamics" is the simplest sort of application [68], and in fact it motivated the present framework.…”

“…The effective physical description consists of an effective energy function and an effective temperature. The transformation between these descriptions will be derived from the elementary Gibbs relation and basic symmetry considerations along lines first explored in [67,68].…”

Effective temperature for finite systems

“…to data from networks and markets, or more generically to large data sets. One such application of immediate interest is to computer network traffic: the use of thermal variables other than entropy to describe computer network traffic has been considered previously [8], [9]. Another area worthy of investigation is temperature in granular media [10], [11].…”

“…where K is a fixed constant with dimensions of action (say, ) whose value we may set to unity w/l/o/g. In the language of an earlier paper [9], ( 12) is a topologically admissible uniform temperature map. This means first that the LHS of ( 12) is bijective in t , which is essentially the zeroth law of thermodynamics, and second that Θ → 0 (resp., ∞) as t ∞ → ∞ (resp., 0).…”

“…Timeinhomogeneous rates q j and probabilities R jk can be readily estimated from the number of connections with origin (type) j and destination (type) k, and this procedure in effect couples the traffic to a Bose gas. [9] In general, most traffic data sets of interest will have a large number of physical or logical addresses and additional metadata which must be aggregated in order to provide a meaningful context for the traffic and to keep B reasonably small. A simple example of this sort of aggregation for computer network traffic will be sketched below.…”