Entropy from Entanglement in Quantum State Reduction

TL;DR

This paper explores how quantum state reduction affects entanglement entropy and thermodynamic entropy, revealing limitations in converting entanglement into usable heat and identifying observable thermodynamic signatures.

Contribution

It demonstrates that entanglement entropy cannot be directly converted into thermodynamic entropy and introduces models linking quantum state reduction to observable thermodynamic effects.

Findings

Entanglement entropy cannot be converted into thermodynamic entropy in a one-to-one manner.

Stochastic dynamics in quantum state reduction allow for multiple entropy definitions.

Models with correlated stochastic forces produce observable thermodynamic signatures.

Abstract

The Von Neumann entropy of reduced states is a measure of bipartite entanglement. Despite its name, the entanglement entropy cannot by itself be used as a resource for creating thermodynamic heat flows. In order to extract heat from an entangled pure state, it first needs to be converted into a stochastically mixed state by a process of quantum state reduction. Here we show that even in a system with only two degrees of freedom, for which bipartite entanglement is the sole form of entanglement available, the entanglement entropy cannot be converted into thermodynamic entropy in a one-to-one fashion. Moreover, we show that the stochastic dynamics which is necessarily present in any realistic model of quantum state reduction, allows for multiple definitions of entropy. We indicate why quantum state reduction does not allow construction of a perpetuum mobile, despite some measures of entropy evolving non-monotonically during its dynamics. Finally, we relate the different measures of entropy to the information they contain about quantum entanglement and extractable heat, and show that models of quantum state reduction based on physical, correlated stochastic driving forces give rise to observable thermodynamic signatures of quantum state reduction that can be unambiguously distinguished from environment-induced dephasing.