Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources

Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system’s initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists.     

The First Butyltin(IV) Homo- and Heterobimetallic Diethanolaminates

Equimolar reactions of BuSn(OPrⁱ)₃ with diethanolamines, RN(CH₂CH₂ OH) ₂ (abbreviated as RdeaH₂, where R = H or Me), afford dimeric isopropoxo-bridged six-coordinate butyltin(IV) complexes [{Bu(η³-Rdea)Sn(μ-OPrⁱ)}₂] (R = H ( 1 ), Me ( 2 )). Interactions between BuSn(OPrⁱ)₃ and diethanolamines (RdeaH₂) in a 1:2 molar ratio yield monomeric derivatives of the type [BuSn(Rdea)(RdeaH)] (R = H ( 3 ), R = Me ( 4 )). These homometallic complexes on 1:1 reactions with an appropriate metal alkoxide form monomeric heterobimetallic complexes of the type [BuSn (Rdea)₂ {M(OR′)_n}] (R = H, M = Al, R′ = Prⁱ, n = 2 ( 5 ); R = H, M = Ti, R = Prⁱ, n = 3 ( 6 ); R = H, M = Zr, R′ = Prⁱ, n = 3 ( 7 ); R = Me, M = Al, R′ = Prⁱ, n = 2 ( 8 ); R = Me, M = Ti, R′ = Prⁱ, n = 3 ( 9 ); R = Me, M = Ge, R′ = Et, n = 3 ( 10 )). The driving force behind this work was (i) to explore the utility of homometal complexes ( 1 ) –( 4 ) in assembling a metal alkoxide fragment via a condensation reaction and (ii) to gain insights into the structures of new compounds by NMR spectral data. All of these derivatives have been characterized by elemental analysis, spectroscopic (IR, NMR; ¹H, ²⁷Al, and ¹¹⁹Sn) studies, and molecular weight measurements. ¹¹⁹Sn NMR spectral studies indicate that both the homometallic ( 3 ) and ( 4 ) and heterobimetallic ( 5 ) – ( 9 ) complexes exist in a solution in an equilibrium of six- and five-coordinated tin(IV) species.     

Heterobimetallic diethanolaminate complexes of titanium and zirconium with alkaline earth metals

Ti(OPr ⁱ )₄ or Zr(OPr ⁱ )₄ · Pr ⁱ OH react with hydrocarbon-insoluble complexes M{(OCH₂CH₂)NH(CH₂CH₂OH)}₂ (M = Mg, Ca, Sr, Ba) in a 2:1 molar ratio to yield hydrocarbon-soluble heterobimetallic diethanolaminate isopropoxide complexes [M{(OCH₂CH₂)₂NH}₂{M(OPr ⁱ )₃}₂] (M = Mg, Ca, Sr, Ba; M = Ti, Zr), which have been characterized by elemental analyses, molecular weight measurements and spectroscopic [i.r., n.m.r. (¹H and ¹³C)] studies.