Research
Some information related to my current research programme can be found here. To find my research papers, please see my arXiv user page, which is updated automatically and contains extended bibliographic details.
I am broadly interested in applying methods from mathematical physics, like geometry, topology, and category theory, to problems in statistical physics, random processes, and probability theory. This consists of further developing the mathematical theory of these areas and applying the resulting tools to make sense of complex or non-equilibrium systems in statistical physics.
Bayesian Mechanics
One of my lower-level interests lies in studying how methods from statistical inference (especially those rooted in geometry or dynamical systems) can yield insights into stochastic analysis, PDE analysis, and statistical physics, especially with respect to complex systems. There is a rich history underwriting this feedback loop, going back to Jaynes, Villani, and others, but the aforementioned results hold at equilibrium, and vast generalisations of those results—or entirely new ones—are needed to cover systems far from equilibrium.
For the last few years I have often worked on ideas related to a certain variational free energy principle for such systems combining information theory and nonequilibrium statistical (especially active and soft matter) physics.
Besides talks about the subject (see my /talks page or my /other page), the following few clusters of papers provide a quick training manual for Bayesian mechanics:
The recent paper A Worked Example of the Bayesian Mechanics of Classical Objects provides a good semi-formal, fast overview of recent progress in Bayesian mechanics, laying out the key ingredients and its connections to other areas of mathematics and physics.
Explicit details and definitions relevant to mode-matching in Bayesian mechanics, and some elaboration on the duality at the centre of Bayesian mechanics, can be found in Towards a Geometry and Analysis for Bayesian Mechanics.
Its connection to control in a worked example of a stochastic process is written about in Bayesian Mechanics for Stationary Processes. Its seemingly proper definition as the laws of motion on a statistical manifold is sketched in Markov Blankets, Information Geometry and Stochastic Thermodynamics.
The fullest single account of (a somewhat more nascent version of) the theory is the 2019 monograph A Free Energy Principle for a Particular Physics. Its initial formulation in terms of coupled random dynamical systems arguably dates back to A Free Energy Principle for Biological Systems.
Its use in stochastic thermodynamics is given in The nonequilibrium statistical mechanics of Markov interacting particles
In the spirit of Example 2.1 and Example 4.1 of the ‘Geometry and Analysis’ paper, a worked example of the Bayesian mechanics of stones is available here.
Other remarks about Bayesian mechanics can be found on my blog.