Postdoctoral Research Associate in Statistical Mechanics

School of Mathematics and Physics
University of Lincoln, United Kingdom

The Centre for Computational Physics at the University of Lincoln is a newly founded research excellence centre focused on the development and application of computational methods to system modelling, material design and foundational issues in statistical mechanics.

We wish to appoint a PDRA to start on October 1^st 2021 for a fixed period of 36 months to work on the Leverhulme funded project RPG-2021-039 titled “Assessing ergodicity in physical systems and beyond”. 

The PDRA will join a friendly community at the School of Mathematics and Physics and be part of the rising University of Lincoln located at the heart of the historic city of Lincoln.

The notion of ergodicity was introduced about 150 years ago by Ludwig Boltzmann to justify a fundamental assumption of his atomistic theory of matter. Nowadays, this notion is framed as the ‘ergodic hypothesis’ and is tacitly assumed in many areas of the quantitative sciences ranging from physics to economics. That the word ‘hypothesis’ remains attached to ergodicity so long after it was introduced reveals a kind of circularity: one presumes ergodicity so that they can use the postulates it was designed to explain in the first place (for example, whether hard sphere systems under Hamiltonian flow are ergodic or not is still an open question).

Much effort has been devoted to overcome this situation. In the 1930s a fruitful dynamical definition of ergodicity has been proposed by Birkhoff. However, this definition appears too strong to be satisfied or even tested in any practical system. Instead, authors such as Khinchin have proposed to view equality between time and ensemble statistics as emerging from generic statistical considerations.

The problem is that real systems are not infinite and neither are the sampled time and ensemble data sets. This gives rise to additional statistical effects, which are currently not accounted for in a systematic manner when discussing ergodicity in a given system.

The project is grounded in an alternative notion of ergodicity, complementary to those of Birkhoff and Khinchin where a time-dependent property is said to have a great degree of ergodicity if a frequency histogram of its values extracted from a single time trajectory has a strong similarity to a histogram extracted from a constraint-satisfying ensemble distribution.

The PDRA will closely work with the Principal Investigator and contribute on all stages of the research project: from mathematically framing ergodicity using the recently developed concepts of fuzzy limits and fuzzy convergence, to the application of the developed methodology to simulated physical and economic models. 

Enquiries about the project have to be sent to the Principal Investigator, Dr. Fabien Paillusson: FPaillusson@lincoln.ac.uk.

The successful candidate should hold a PhD in a relevant area of Physics or Applied Mathematics (or a thesis submitted by the start date of the position).