One-Shot Information-Theoretical Approaches to Fluctuation Theorems

Abstract

Traditional thermodynamics governs the behaviour of large systems that evolve between states of thermal equilibrium.For these large systems, the mean values of thermodynamic quantities (such as work, heat and entropy) provide a good characterisation of the process.Conversely, there is ever-increasing interest in the thermal behaviour of systems that evolve quickly and far from equilibrium, and that are too small for their behaviour to be well-described by mean values. Two major fields of modern thermodynamics seek to tackle such systems: non-equilibrium thermodynamics, and the nascent field of one-shot statistical mechanics. The former provides tools such as fluctuation theorems, whereas the latter applies "one-shot" Rényi entropies to thermal contexts. In this chapter of the upcoming book "Thermodynamics in the quantum regime -Recent progress and outlook" (Springer International Publishing), I provide a gentle introduction to recent research that draws from both fields: the application of oneshot information theory to fluctuation theorems.

Fundamental limitations on photoisomerization from thermodynamic resource theories

“…D max is well-defined if the first state's support lies in the second state's: supp(ρ) ⊆ supp(σ). This entropy quantifies how well ρ and σ can be distinguished in a particular trial of state discrimination [142].…”