Beyond the Arrow of Time: Can There Be a Relation between the Measurement of Entropy and Time?

Abstract

Abstract:The general tendency of the entropy of an isolated to increase is considered to be directly linked to the direction of the flow of time. This raises the question whether a quantitative relation can be established such that a time interval can be measured by measuring entropy change and vice versa. The existence or absence of such a link also calls for further consideration of the nature of time. Prigogine argued that the true nature of time can only be discovered by investigating this phenomenon using scientific and philosophical methods. If this is true, then ongoing debates in the metaphysics of time and progress in the scientific study of entropy can be brought together to shed light on this fascinating but elusive concept. In this paper, starting from my recent modified definition of entropy change as a non-dimensional measure of energy change, a direct link between entropy and time duration is suggested. It draws from steady energy transfer processes such as heat transfer and shows that a measure of time can be found to be associated with a measure of entropy change. In the absence of other driving forces, the passage of time in an isolated system can therefore be tracked with a well calibrated entropy change meter. When other forces are allowed to interfere and there is no external point from which the system can be considered to be isolated, then the measure of time is non-monotonous since an isolated system can be restored to an earlier state of non-equilibrium. More philosophical questions about time can be reduced to questions about the operation of memory and consciousness, whereby psychological awareness of time is in essence a mental awareness of the way things are ordered by direct perception and memory of how they were ordered in the past, permitting a measure of the departure between things changing with greater or lesser intensity.

Assessing time series irreversibility through micro-scale trends

“…In order to understand why an irreversibility metric may fail at correctly classifying a time series, let us introduce the concept of permutation patterns, initially proposed to assess the degree of complexity (or determinism vs. stochasticity) of time series 28,29 . Given a (usually short) window, the corresponding permutation pattern is defined as the order that has to be applied to its elements to sort them -such that, for instance, the pattern associated to values (8,4,5) would be (2, 3, 1), as the second element is the smallest one, followed by the third and the first. It has recently been proposed that such patterns can be used to assess irreversibility.…”

“…In spite of some important advantages, like their simplicity and reduced computational cost, permutation patterns also present the drawback of disregarding the amplitude of the signal -to illustrate, the two time series (8,4,5) and (16,8,10) will always result in the same pattern. This well-known fact has important consequences in the estimation of the associated entropy 30,31 ; but further leads to situations in which an irreversible time series may be classified as not irreversible, only because such irreversibility manifests itself in amplitude.…”