Quantum and classical ergotropy from relative entropies

Abstract

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. We prove that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state. This insight is exploited to define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both, quantum as well as classical scenarios, is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.

Harmonic flow field representations of quantum bits and gates

“…The qubit analogy also presents an opportunity to extend a previously noted correspondence between quantum theory and classical statistical mechanics [43]. In particular, the mappings presented here raise the interesting question of how defect entanglement and entanglement entropy [44,45] could be generalized to flow and deformation fields in more complex fluids and continuum systems, including passive [46] and active [47] liquid crystals and membranes [48].…”

Quantum Euler relation for local measurements

“…The maximum amount of work that can be extracted from the composite state ρ AB , through unitary and cyclic operations, is referred to as the ergotropy "E " [26,49,50]. Consider a quantum system with Hamiltonian H = ∑ d i=1 ε i |ε i ε i | and quantum state ρ = ∑ d j=1 r j r j r j , such that ε i ≤ ε i+1 and r j ≥ r j+1 .…”