Abstract
There are many ways to decompose the Hilbert space 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 . 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. ). 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.
Highlights
More than fifty years ago, it was noted in the context of quantum electrodynamics that there is an inherent relativity present within the definition of a quantum subsystem (1, 2)
Assumes the bare energy operators Ha and Hb represent the observable energies of the subsystems, the results in Section 3.2 show that the CSL is genuinely violated, albeit transiently, within certain parameter regimes and for certain interaction Hamiltonians
There is experimental evidence to support such violations (20, 21). If such violations are viewed as untenable, even transiently, either the physically available interactions between quantum subsystems become limited by the CSL, or one must reject the physicality of the free energy operators as representing observable energies
Summary
More than fifty years ago, it was noted in the context of quantum electrodynamics that there is an inherent relativity present within the definition of a quantum subsystem (1, 2). We propose applying Clausius’ form of the second law of thermodynamics (CSL) in quantum physics to restrict the possible forms of quantum interactions and subsystem decompositions of composite quantum systems. Our focus here is on the Clausius form of the second law for interacting elementary systems initially in contact with separate heat baths so as to be prepared in thermal states These are isolated and allowed to evolve. Weimer et al have developed an energy-flux formalism based on the local measurement basis (LEMBAS) principle, which they use to give general definitions of heat and work within the interacting setting (27) This formalism is further studied and extended to include open quantum systems in (28), where it is shown to give rise to an entropic version of the second law.
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