Using thermodynamics to identify quantum subsystems

Abstract

There are many ways to decompose the Hilbert space $\mathcal{H}$ of a composite quantum system into tensor product subspaces. Different subsystem decompositions generally imply different interaction Hamiltonians V, and therefore different expectation values for subsystem observables. This means that the uniqueness of physical predictions is not guaranteed, despite the uniqueness of the total Hamiltonian H and the total Hilbert space $\mathcal{H}$. Here we use Clausius’ version of the second law of thermodynamics (CSL) and standard identifications of thermodynamic quantities to identify possible subsystem decompositions. It is shown that agreement with the CSL is obtained, whenever the total Hamiltonian and the subsystem-dependent interaction Hamiltonian commute (i.e. $[H,V]=0$). Not imposing this constraint can result in the transfer of heat from a cooler to a hotter subsystem, in conflict with thermodynamics. We also investigate the status of the CSL with respect to non-standard definitions of thermodynamic quantities and quantum subsystems.

Keywords:

• Quantum electrodynamics
• quantum thermodynamics
• anomalous heat flow

Notes

No potential conflict of interest was reported by the authors.

1 Here we are adopting an active view towards unitary transformations within the composite system’s Hilbert space. This means that the Hamiltonian is actively transformed into a new unitarily equivalent Hamiltonian. In the introduction 1 we adopted a passive viewpoint towards unitary transformations, in which the same Hamiltonian was expressed in different operator bases. The active and passive perspectives are of course equivalent for understanding quantum subsystem relativity.

Additional information

Funding

AS and AB acknowledge financial support from the UK Engineering and Physical Sciences Research Council EPSRC [grant number EP/H048901/1]; [grant number EP/M013243/1]. PD thanks the British Council and DST Government of India for financial support. Statement of compliance with EPSRC policy framework on research data: This publication is theoretical work that does not require supporting research data.