Fluctuation Theorems in Quantum Resource Theories

Alvaro Alhambra
July 3rd, 2018 ALVARO ALHAMBRA Perimeter Institute

The Jarzynski and Crooks fluctuation theorems are two very important equalities that appear in the context of stochastic thermodynamics. These control the non-equilibrium fluctuations of work in stochastic processes, in a way much stronger than the second law. One of the ongoing research lines that these results have set off is that of understanding the right quantum analogues of such fluctuation theorems. We here suggest a particular way to answer this problem, embedded within the quantum resource theory of thermodynamics, a framework for analizing non-equilibrium quantum dynamics which is heavily inspired by the theory of quantum entanglement. In doing so we see how the Petz map, a non-commutative generalization of “Bayesian inversion” of classical conditional probabilities, naturally appears in the formulation of these theorems.

We further show how to exploit the structural similarities between the resource theories of thermodynamics and of pure bipartite entanglement to derive an entanglement analogue of work fluctuations, from which one obtains analogous statements to those of Jarzynski and Crooks’. These "fluctuations” are now a type of resource, akin to embezzling states, that serve to extend the set of possible transitions between entangled states at the single-copy level.

Joint work with Jonathan Oppenheim, Lluis Masanes and Chris Perry

Seminar, July 3, 2018, 16:00. ICFO’s Seminar Room

Hosted by Prof. Antonio Acín