Fraser Sanders: Infinite-dimensional thermodynamic systems
| Dates: | 26 October 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Speaker: | Fraser Sanders (Manchester) |
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Abstract:
Contact geometry is a very natural setting in which to study thermodynamics, due to the fact that the first law of thermodynamics, dS=dU/T , can be thought of as constraining the dynamics of a system to a contact distribution in 3 dimensions, defined by the kernel of the contact 1-form \eta=dS - (1/T)dU , and then many interesting properties of thermodynamic systems arise from the non-holonomic constraints.
In recent months (due to Boris Khesin, Manuel de León, myself, and others) there has been an increasing interest in infinite-dimensional contact and non-holonomic systems, and their associated dynamics. Both because there are many infinite-dimensional physical systems that are dissipative in nature, and hence well-suited to being modelled by contact dynamics, and because there are some systems, such as Black Holes, which are supposed to be thermodynamic systems, but which have such high degrees of freedom that they may also be modelled in infinite-dimensions (ignoring the No-Hair Theorem, at least…).
In this talk I will discuss infinite-dimensional contact structures, their associated Hamiltonian mechanics, and how we can use these concepts to try to justify talking about so-called infinite-dimensional thermodynamic systems. Time-permitting (meaning, if I can write the result down in the coming week) I will discuss Ricci flow as an example of such a system, as a stepping-stone towards Black Hole thermodynamics. Other examples include the damped wave equation, and the heat equation.
Speaker
Fraser Sanders (Manchester)
Travel and Contact Information
Find event
Frank Adams room 1
Alan Turing Building
Manchester
