Individual components such as cells, particles, or agents within a larger system often require detailed understanding of their relative position to act accordingly, enabling the system as a whole to function in an organised and efficient manner. Through the concept of positional information (PI), such components are able to specify their position in order to, e.g., create robust spatial patterns or coordinate specific functionality. In this talk, I will introduce PI in the setting of non-equilibrium lattice gases and show how it can be computed and bound using two basic tenets of statistical physics, namely stochastic thermodynamics and interacting particle systems.
We first establish that close to equilibrium, a local-equilibrium description leads to a universal PI determined only by the chemical potential and density gradients, independent of microscopic details of the model. We then test this result on several interacting particle models such as exclusion and inclusion processes and the zero-range process, and find that the near-equilibrium expression serves as an upper bound on PI in the far-from-equilibrium regime. Overall, our framework exposes a fundamental physical limit on how much positional information can be encoded in non-equilibrium steady states. Finally, I will present my future plans at RRI.