Related papers: Clock Time and Entropy
We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
Using mobile phone records and information theory measures, our daily lives have been recently shown to follow strict statistical regularities, and our movement patterns are to a large extent predictable. Here, we apply entropy and…
The paper puts forward a conceptual framework in which the phenomenon of time can be presented and discussed in a proper way. We argue that change is ontologically and epistemologically a more basic phenomenon than time. Time is an abstract…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time…
I show that the clock ambiguity cannot be solved by a purely relational condition like the noninteraction condition, and it is even stronger, extending to evolution laws. The ambiguity is solved by specifying the physical meaning of…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
In this work we scrutinize the deterministic nature of globally hyperbolic space-times from the point of view of an observer. We show that a space-time point $q \in M$ that lies to the future of an observer at $p \in M$, receives signals…
Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.
We compare the sensitivity of a recent bound on time variation of the fine structure constant from optical clocks with bounds on time varying fundamental constants from atomic clocks sensitive to the electron-to-proton mass ratio, from…
The flowfield resulting from a starting source type singularity is presented. This is a generalization of the classical source in potential flow to time dependent situations, including sources in oncoming flow. This model is applicable to…
We show that if one or more of the `constants' of Nature can vary then their values, as measured in the laboratory, should oscillate over the year in a very particular way. These seasonal changes in the constants could well be detected, in…
We study the notion of a causal time-evolution of a conserved nonlocal physical quantity in a globally hyperbolic spacetime $\mathcal{M}$. The role of the `global time' is played by a chosen Cauchy temporal function $\mathcal{T}$, whereas…
It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively…