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Decomposing the Local Arrow of Time in Interacting Systems
Christopher W Lynn1,2, Caroline M Holmes2, William Bialek1,2
1Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA.
Physical Review Letters
|September 26, 2022
Summary
The arrow of time, or entropy production, can be broken down into contributions from individual variables and their correlations. This reveals how neural activity in the retina generates irreversibility through neuronal interactions.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Computational Neuroscience
Background:
- The arrow of time is fundamentally linked to entropy production in thermodynamic systems.
- Understanding the origins of irreversibility in complex systems is a key challenge.
- Previous work has explored entropy production but lacked a detailed decomposition of correlational contributions.
Purpose of the Study:
- To decompose the evidence for a local arrow of time into contributions from individual variables and their correlations.
- To investigate the sources of irreversibility in biological systems, specifically neural activity.
- To analyze how correlations in neural activity contribute to the overall system's irreversibility.
Main Methods:
- Developed a theoretical framework to decompose entropy production into individual and correlational terms.
- Applied this decomposition to models of noisy logical computations.
- Analyzed patterns of neural activity in the retina using dynamic visual stimuli.
Main Results:
- Demonstrated that entropy production can be decomposed into a sum of non-negative terms.
- Showed that correlations among variables (pairs, triplets, etc.) contribute to irreversibility.
- Found that retinal neural activity breaks detailed balance independently of visual input, with pairwise neuronal interactions being the primary source of irreversibility.
Conclusions:
- The theoretical framework provides a novel way to quantify irreversibility in complex systems.
- Neural systems exhibit intrinsic irreversibility driven by interactions, even when external stimuli are reversible.
- Pairwise neuronal interactions are critical drivers of the arrow of time in the retina.
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