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arXiv:1804.04182 · Physics Letters A

Principle of Unattainability of absolute zero temperature, the Third Law of Thermodynamics, and projective quantum measurements

Tien D. Kieu

Published Jul 22, 2019• 5 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2019.125848

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1 entropy and the laws of thermodynamics 1 1.1 Entropy 2 1.1.1Classical and Statistical Entropy 4 1.1.2Aspects of Entropy 6 1.2 The 0th Law 7 1.3The 1st Law 7 1.4The 2nd Law 8 2 the third law 11 2.1 Consequences of the Third Law 12 2.2 Helium and the Third Law 14 2.3 Non-Equilibrium Degrees of Freedom 15 2.4 The Unattainability of Absolute Zero 19 3 violations of the laws of thermodynamics 23 3.1 The Second Law 23 3.1.1Fluctuations 24 3.2 The Third Law 26 4 the boson driven refrigerator 29 4.1 Introduction of the Refrigerator Model 29 4.2 Discussion 30 4.3 Non-Equilibrium Systems and Thermodynamics 36 4.4 Objective 37 5 non-equilibrium thermodynamics 39 5.1 The Stochastic Master Equation 40 5.2 Local Detailed Balance 41 5.3 The Stochastic Laws of Thermodynamics 42 5.3.1 The First Law 42 5.3.2The Second Law 43 5.4 Tight Coupling and Efficiency 45 6 boson powered refrigeration 49 6.1 Particle Currents 49 6.2 Heat Transport and Effieciency 52 6.3 Cooling power in the Limit of Absolute Zero 56 7 numerically optimized cooling 59 7.1 Conditions for Optimized Cooling 59 7.2 The Very Low Temperature Regime 63 8 finite energy level spacing 67 8.1 Dependency on δ and ∆ 73 8.2 Maximized Cooling Power 75 8.3 Higher Order Transitions 79 VII VIII contents 8.4 Heat Capacity of the Discrete Model 80 8.5 The Unattainability of Absolute Zero 82 9 summary 85 9.1 Summary and Conclusions 85 9.2 Discussion 86 9.3 Recommendations for Further Work 87 a appendix 89 a.1 C++ Source Code for the Continuous Model 89 a.2 C++ Source Code for the Discrete Model 96

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Abstract The third law of thermodynamics has two classical formulations: Nernst’s heat theorem (entropy change ΔS→0 as T→0) and the unattainability principle (absolute zero cannot be reached in a finite number of steps). Quantum statistical mechanics challenges Nernst’s theorem through residual entropy in systems such as quantum spin liquids and spin ice, which retain nonzero entropy even as T→0. Landauer’s principle connects information erasure with heat dissipation, implying that reaching absolute zero is equivalent to deleting all information from a system. This paper proposes that physical reality comprises two information-carrying sectors—the material phase (Ξ) and the information phase (Ω)—governed by strict conservation of total information. Within this framework, absolute zero is reinterpreted as the global information ground state of two-phase information settlement: it is both the absolute zero point of material-phase information capacity and the material embodiment of the minimal information potential of the information phase. Residual entropy is not an exception to the third law, but an inevitable manifestation of information conservation at the absolute zero boundary. Starting from the principle of least action incorporating two-phase coupling, we derive a quantitative condition for the unattainability of absolute zero and demonstrate that the decoherence rate of a quantum system near absolute zero is systematically modulated by the information-phase coupling parameter. The framework yields three testable predictions: a scaling relation between decoherence rate and information-phase coupling strength at ultra-low temperatures, entropy accumulation near quantum critical points corresponding to enhanced information-phase potential density, and a temperature scaling law for the coherence time of time crystals. This work unifies the third law of thermodynamics with quantum measurement, black hole information processing, dark energy cosmology, quantum entanglement, and the Higgs mechanism under a single cross-scale information settlement paradigm. Keywords: absolute zero, third law of thermodynamics, residual entropy, information conservation, Landauer’s principle, decoherence, quantum spin liquid, time crystal
One of the formulations of the third laws of thermodynamics is that a processes become more isentropic as one approaches the absolute zero temperatures. We examine this prediction by studying an operating model of a quantum refrigerator pumping heat from a cold to a hot reservoir. The working medium consists of a gas of noninteracting harmonic oscillators. The model can be solved in closed form in the quasi-static limit or numerically for general conditions. It is found that the isentropic limit for Tc → 0 is approached only on the expansion segment of the refrigeration cycle. The scaling of the cooling rate with temperature is shown to be consistent with the second law of thermodynamics. This scaling is also consistent with the unattainability principle which is an alternative formulation of the third law of thermodynamics.
1 entropy and the laws of thermodynamics 1 1.1 Entropy 2 1.1.1Classical and Statistical Entropy 4 1.1.2Aspects of Entropy 6 1.2 The 0th Law 7 1.3The 1st Law 7 1.4The 2nd Law 8 2 the third law 11 2.1 Consequences of the Third Law 12 2.2 Helium and the Third Law 14 2.3 Non-Equilibrium Degrees of Freedom 15 2.4 The Unattainability of Absolute Zero 19 3 violations of the laws of thermodynamics 23 3.1 The Second Law 23 3.1.1Fluctuations 24 3.2 The Third Law 26 4 the boson driven refrigerator 29 4.1 Introduction of the Refrigerator Model 29 4.2 Discussion 30 4.3 Non-Equilibrium Systems and Thermodynamics 36 4.4 Objective 37 5 non-equilibrium thermodynamics 39 5.1 The Stochastic Master Equation 40 5.2 Local Detailed Balance 41 5.3 The Stochastic Laws of Thermodynamics 42 5.3.1 The First Law 42 5.3.2The Second Law 43 5.4 Tight Coupling and Efficiency 45 6 boson powered refrigeration 49 6.1 Particle Currents 49 6.2 Heat Transport and Effieciency 52 6.3 Cooling power in the Limit of Absolute Zero 56 7 numerically optimized cooling 59 7.1 Conditions for Optimized Cooling 59 7.2 The Very Low Temperature Regime 63 8 finite energy level spacing 67 8.1 Dependency on δ and ∆ 73 8.2 Maximized Cooling Power 75 8.3 Higher Order Transitions 79 VII VIII contents 8.4 Heat Capacity of the Discrete Model 80 8.5 The Unattainability of Absolute Zero 82 9 summary 85 9.1 Summary and Conclusions 85 9.2 Discussion 86 9.3 Recommendations for Further Work 87 a appendix 89 a.1 C++ Source Code for the Continuous Model 89 a.2 C++ Source Code for the Discrete Model 96