"Thermodynamic potential” for a class of non-equilibrium systems

Although basic equilibrium concepts like state variables, thermodynamic potentials, etc do not straightforwardly extend for non-equilibrium states, an analogue of Landau free energy characterising macroscopic fluctuations could be defined based on a mathematical theory of large deviations. I shall present exact results for such a quantity in a class of non-equilibrium transport models. These are interacting many-body systems related to SU(2) and SU(1,1) spin chains. Our results show that, similar to a thermodynamic potential, these free-energy-analogues are robust against variations of coupling with external bath, thereby strengthening the possibility of a thermodynamic description for non equilibrium states.

I shall explain how these exact results are derived using a matrix-product-representation for a specific integrable model [1]. Then, I shall recover these results using a minimal action solution of a hydrodynamic theory [2], which applies to a wider class of systems, including those which are non-integrable.

Ref. [1] Derrida, Hirschberg, Sadhu, 182 (2021) J Stat Phys
        [2] Sadhu, unpublished.