The Department of Physics is delighted to welcome Prof Alexander Schekochihin (University of Oxford) to give the twelfth Physics Department Colloquium of Semester 2 2023/24. Please join us to listen to Prof Alexander Schekochihin's seminar titled 'In search of universality: towards a statistical mechanics of collisionless plasma'.

A reception will be held directly after the seminar, where tea and coffee will be provided.

The seminar is open to anyone from the university, students are encouraged to attend.

# Title

In search of universality: towards a statistical mechanics of collisionless plasma

# Abstract

Much of existing plasma (astro)physics is done hovering in the vicinity of a Maxwellian equilibrium, which is the maximum point of the standard Gibbs entropy and is achieved dynamically by means of two-particle collisions. In this colloquium, I would like to discuss what I believe to be the next frontier for (astro-)plasma theoreticians — and, to an extent, generally fir theoretical physicists concerned with complex many-body systems — and attempt to grapple with the fact that many natural plasmas are too collisionless to be Maxwellian (in the sense that their dynamics occur on shorter timescales than interparticle collisions). The central question is then whether there exist universal collisionless equilibria, or classes thereof, and what they are. What is the meaning of entropy in a collisionless plasma? (Similar questions are asked in galactic dynamics, where the collisionless particles are stars.) I will discuss some simple ideas, going back to the work of Lynden-Bell in the 1960s, about the statistical mechanics of collisionless systems, leading to a class of universal collisionless equilibria — these are reminiscent of the equilibria of Fermi gases, with phase-volume conservation imposing (an infinite set of) Casimir invariants, whose effect is analogous to that of the Pauli exclusion principle. The generalised Lynden-Bell equilibria obtained in this way cover quite a wide variety of distributions — most intriguing perhaps is that they will generically feature “nonthermal” power-law tails [1] — a matter of some interest, e.g., for the theory of cosmic rays and of the nonthermal particle distributions routinely measured in the solar wind, as well as in statistical mechanics of various soft-matter systems. I will then outline a programme for how one might do to this statistical mechanics what Boltzmann did to Gibbs: derive a “collisionless collision integral” that describes the dynamical relaxation of a plasma towards the Lynden-Bell equilibria. It turns out that in order to make progress in this task, one must understand the structure of chaotic fluctuations in phase space. Lynden-Bell-like equilibria are recoverable under some very restrictive assumptions — roughly speaking, when these fluctuations are treated as structurally similar to a thermal noise [2]. In fact, they are more likely to behave like fully-fledged turbulence — with phase mixing (“Landau damping”) and stochastic echoes conspiring to process a constant flux of energy [3]. What universal equilibria (if any) exist against such a background is a topic of ongoing research.

**References**

[1] R. J. Ewart, M. L. Nastac, and A. A. Schekochihin, J. Plasma Phys. 89, 905890516 (2023) [e-print arXiv:2304.03715]

[2] R. J. Ewart, A. Brown, T. Adkins, and A. A. Schekochihin, J. Plasma Phys. 88, 925880501 (2022) [e-print arXiv:2201.03376]

[3] M. L. Nastac, R. J. Ewart, W. Sengupta, A. A. Schekochihin, M. Barnes, and W. D. Dorland, PRE, in press [e-print arXiv:2310.18211]