Abstract:
A fundamental feature of thermodynamic systems consisting of many components is the self-averaging property: the densities of macroscopic quantities are sharply peaked around their most probable values (Laws of large numbers). Typical fluctuations around these values are of the order of the square root of the volume and have a Gaussian shape (Normal central limits). In contrast, macroscopic fluctuations occur rarely, with exponentially suppressed probabilities. It is well known for the classical equilibrium systems that the decay rates for these probabilities coincide with certain thermodynamic potentials (Large-deviation principles). In my talk, I will explain how the large deviation probabilities can be computed in certain quantum spin models, by using perturbation expansions and the Gartner-Ellis theory [1]. In particular, a natural quantum modification of the large-deviation principle emerges there. The large-deviation formalism is not restricted to the equilibrium set-up and, as another application, I will show that it is also a natural framework in which the Evans-Gallavotti-Cohen fluctuation symmetry for the entropy production in open thermodynamic systems [2], and the Jarzynski equality for the non-equilibrium thermodynamic processes [3] can be formulated. An open problem is to study the correlated macroscopic fluctuations for a collection of mutually noncommuting macro-observables.
References:
[1] K. Netocny and F. Redig. J. Stat. Phys. 117:521-547 (2004).
[2] G. Gallavotti and E. G. D. Cohen. Phys. Rev. Lett. 74:2694-2697 (1995).
[3] C. Jarzynski. Phys. Rev. Lett. 78:2690-2693 (1997).