On the Entropy Production of Time Series with Unidirectional Linearity

By Dominik Janzing. 2009

10 citations recorded by the source corpus.

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are not statistically independent of the regressor. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry.For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we argue that unidirectional linearity is also accompanied by entropy generation.To this end, we study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited by the forward-time conditional probabilities, but not by the backward-time conditionals. The reason is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependence afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward process to the minimal amount of entropy generation.The paper thus shows that unidirectional linearity is an indirect implication of the thermodynamic arrow of time, given that the joint dynamics of the system and its environment is linear.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. B. Schoelkopf
2. Rafael Chaves
3. Bernhard Schölkopf
4. Dominik Janzing
5. Tameem Albash
6. Daniel A. Lidar

In Statistical and Nonlinear Physics

1. Rafael Chaves
2. B. Schoelkopf
3. Bernhard Schölkopf
4. Dominik Janzing
5. Manuel Gomez-Rodriguez
6. Jure Leskovec

Citations in the corpus

• Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference (2015, background): “In particular, a physical toy model relating such asymmetries to the usual thermodynamic arrow of time has been proposed [17].”
• Causal Inference Using the Algorithmic Markov Condition (2008, background): “[42] describes a physic al toy model that provides a thermodynamical justification, but the relation of these results to the algorithmic Markov condition is not obvious.”