Fluctuation theorems and thermodynamic uncertainties in the presence of mesurement and feedback
Due to significant theoretical and experimental advances, today we are able to measure and control systems at the level of individual molecules and atoms. In this scenario, in addition to exhibiting genuinely quantum properties, the systems are out of thermal equilibrium, making energy fluctuations inevitable. Thus, it is necessary to describe magnitudes arising from thermodynamics such as work, heat and entropy through stochastic quantities, that is, through probability distributions.
In this direction, the development of relations or fluctuation theorems has become fundamental for us to understand the behavior and correlations between stochastic thermodynamic observables. In addition to providing new insights into the origins of irreversibility, energy dissipation processes and generalizations of the second law of thermodynamics for systems far from equilibrium, the buoyancy relations allow us to analyze the measurement process followed by a conditioned operation, known as feedback or feedback, in order to quantify the consequences of treating information as a resource in physical processes.
In this work, we present two experimental studies using the nuclear magnetic resonance technique. The first focuses on verifying a fluctuation relationship in a quantum scenario that has control and feedback. Although, there are many theoretical proposals to verify fluctuation theorems in the presence of feedback, as far as we know, this is the first experimental demonstration using nuclear spins. The second focuses on testing the robustness of a set of inequalities, which establish a connection between the fluctuation of thermodynamic quantities and the dissipation during a stochastic process, called thermodynamic uncertainty relations, against the asymmetry caused by a measurement process and feedback.