Two State Weak and Mean Valued Energy Quantum Systems are Thermodynamically Homologous

Authors : Allen D PARKS

Pages : 121-128

Doi:10.5541/ijot.5000176048

View : 11 | Download : 5

Publication Date : 2016-05-25

Article Type : Research Paper

Abstract :Canonical ensemble theory is used to obtain simple exact scaling relationships insert ignore into journalissuearticles values(homology transformations); which establish equivalences between certain thermodynamic quantities for two state weak valued and mean valued energy quantum systems that are described by the same Hamiltonian. These equivalences define how a thermodynamic quantity for a weak insert ignore into journalissuearticles values(mean); valued energy system can be represented by an appropriately scaled version of the same quantity for a mean insert ignore into journalissuearticles values(weak); valued energy system. This provides: insert ignore into journalissuearticles values(i); a method for quantifying the thermodynamic properties of the typically more complicated insert ignore into journalissuearticles values(and difficult to prepare); weak valued energy systems in terms of those of the generally less complicated mean valued energy systems; and insert ignore into journalissuearticles values(ii); a systematic way to compare the properties of weak and mean valued energy systems. The results are validated and illustrated numerically by applying them to a spin ½ system in a uniform magnetic field. Several apparent thermodynamic effects induced by the weak measurement and state post-selection process required to prepare a weak valued energy system are also identified for this system.
Keywords : Thermodynamics, Weak Energy, Mean Energy, Homology Transformations, 2 State Quantum Systems