Inequalities in Rényi's quantum thermodynamics

Abstract

A theory of thermodynamics has been recently formulated and derived on the basis of Rényi entropy and its relative versions. In this framework, we define the concepts of partition function, internal energy and free energy, and fundamental quantum thermodynamical inequalities are deduced. In the context of Rényi's thermodynamics, the variational Helmholtz principle is stated and the condition of equilibrium is analyzed. The Rényi maximum entropy principle is formulated and the equality case is discussed. The obtained results reduce to the von Neumann ones when the Rényi entropic parameter $α$ approaches 1. The Heisenberg and Schrödinger uncertainty principles on the measurements of quantum observables are revisited. The presentation is self-contained and the proofs only use standard matrix analysis techniques.