P.S. This work was inspired in large part by one of my favorite mathematical biology papers of the 20th century, "Will a Large Complex System be Stable", published by Robert May in 1972.
www.nature.com/articles/238...
I highly recommend checking it out if you haven't read it!
Thanks to Yale's Department of Physics and Quantitative Biology Institute, and the Natural Sciences and Engineering Research Council of Canada (NSERC) for supporting my research!
These results indicate that Maxwell demons cannot arise by chance in systems with many degrees of freedom, so we should be surprised when we find demons in the wild! This ultimately suggests that Maxwell demons can only arise through some process of selection.
For a large class of models, both analytic and numerical results show that the probability of finding a Maxwell demon by chance decreases at least exponentially, and in some cases even double-exponentially, with the number N of degrees of freedom -- becoming vanishingly unlikely.
So how likely is it that a random complex system with N degrees of freedom will operate as a Maxwell demon? To address this I formulate null models for random dynamics with both continuous and discrete degrees of freedom, and calculate the probability p(demon|N).
A Maxwell demon is a multi-component thermodynamic system where at least one subsystem takes in heat from its environment, thus appearing in isolation to locally violate the 2nd law of thermodynamics. The 2nd law is recovered by accounting for information flow between subsystems.
I tackle this question in a new preprint: Will a Large Complex System be a Maxwell Demon?
arxiv.org/abs/2603.03248
The spectre of Maxwell’s demon looms all around us, with sightings reported across diverse fields from economics, to evolutionary biology, to cellular sensing, to molecular biophysics. But how surprised should we be to find demons haunting the physical world?
Thanks again to NSERC, the Canada Research Chairs program, and @sfuphysics.bsky.social for supporting our research, and thanks to @mitacscanada.bsky.social for funding Julián’s time as a visiting researcher in the Sivak Group.
Check it out here: journals.aps.org/prresearch/a..., or see my previous thread for more details: bsky.app/profile/mlei...
Out today in @physrevresearch.bsky.social: "Information Thermodynamics of Cellular Ion Pumps", led by Julián Jiménez-Paz (@cornelluniversity.bsky.social), with @davidasivak.bsky.social (@sfuphysics.bsky.social)!
Last call for postdoctoral applications to join my group at University of Toronto. Feel free to reach out if you want to learn more about the position.
Postdoctoral Job Opportunity! I am hiring a postdoc to join my group next fall. Many possible research directions in theoretical biophysics and nonequilibrium statistical mechanics. See the posting linked below for details — apply by Jan 15th for full consideration.
Finally, thanks to Yale's Department of Physics and Quantitative Biology Institute, and the Natural Sciences and Engineering Research Council of Canada (NSERC) for supporting our work!
The non-Markovian dynamics of biological systems arise from coarse-graining the underlying fundamental physics to produce simplified descriptions. Going forward, our work paves the way to study how non-Markovian dynamics emerge through coarse-graining across scales. Stay tuned!
This is roughly the timescale biologists have identified as the length of the fly’s working memory for both odor sensing and navigation, which we’ve detected using only recorded behavior data! This hints that memory is the main driving factor for the fly’s non-Markovian behavior.
We then turn to biological data, 400,000 minutes of recorded fruit fly behavior with 10ms time resolution. Our most intriguing result: we discover a unique timescale that maximizes how much information the fly’s past behavior holds about its future behavior, about 7 seconds.
We first explore analytically-tractable minimal models for non-Markovian dynamics. This lets us build intuition for the highly counterintuitive behavior of non-Markovian dynamics with long-range history dependence. E.g.: autocorrelations can fail to reflect true dependencies!
We develop new information-theoretic tools to
1. Quantify how strongly the dynamics of biological systems depend on their past.
2. Decompose this dependence into contributions from different parts of the past, quantifying the information you gain by learning each past state.
arxiv.org/abs/2512.13933
arxiv.org/abs/2512.13936
The fundamental laws of physics are Markovian: the next state of a physical system depends only on its current state. Biology, however, is often non-Markovian: the next state can depend on states arbitrarily far back into the past.
Excited to share two final preprints for the year:
“Decomposing Non-Markovian History Dependence”,
and
“Tractable Model for Tunable Non-Markovian Dynamics”.
Both with chriswlynn.bsky.social.
This is roughly the timescale biologists have identified as the length of the fly’s working memory for both odor sensing and navigation, which we’ve detected using only recorded behavior data! This hints that memory is the main driving factor for the fly’s non-Markovian behavior.
We then turn to biological data, 400,000 minutes of recorded fruit fly behavior with 10ms time resolution. Our most intriguing result: we discover a unique timescale that maximizes how much information the fly’s past behavior holds about its future behavior, about 7 seconds.
We first explore analytically-tractable minimal models for non-Markovian dynamics. This lets us build intuition for the highly counterintuitive behavior of non-Markovian dynamics with long-range history dependence. E.g.: autocorrelations can fail to reflect true dependencies!
We develop new information-theoretic tools to
1. Quantify how strongly the dynamics of biological systems depend on their past.
2. Decompose this dependence into contributions from different parts of the past, quantifying the information you gain by learning each past state.
arxiv.org/abs/2512.13933
arxiv.org/abs/2512.13936
The fundamental laws of physics are Markovian: the next state of a physical system depends only on its current state. Biology, however, is often non-Markovian: the next state can depend on states arbitrarily far back into the past.
Johann du Buisson, Jannik Ehrich, mleighton.bsky.social, davidasivak.bsky.social, and John Bechhoefer introduce a one-coordinate test that infers heat flow to flag “demonic” operation. In kinesin simulations tuned to experiments, the motor grows more demon-like as active fluctuations rise.
Our recent work (elifesciences.org/articles/104...) combines theory and experiments (by Alex Papagiannakis and Christine Jacobs-Wagner) to understand how chromosome segregation is coupled to growth in E coli. We demonstrate that the nonequilibrium dynamics of polysomes may play a key role.
Thanks to NSERC, the Canada Research Chairs program, and @sfuphysics.bsky.social for supporting our research! Special thanks to @mitacscanada.bsky.social for funding Julian’s time as a visiting researcher in the Sivak Group last Summer.
Over the voltage range typical of a neuronal action potential, at low voltages the pump exhibits Maxwell-demon behavior and high efficiency, while at high voltages the pump instead operates as a conventional engine and achieves higher turnover at the cost of lower efficiency.
