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
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
The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near to absolute zero. On the other hand, a fundamental assumption of quantum computing is to start each computation from a register of qubits initialized in a pure state, i.e., at zero temperature. These conflicting aspects, at the interface between quantum computing and thermodynamics, are often overlooked or, at best, addressed only at a single-qubit level. In this Letter, we argue how the existence of a small but finite effective temperature, which makes the initial state a mixed state, poses a real challenge to the fidelity constraints required for the scaling of quantum computers. Our theoretical results, carried out for a generic quantum circuit with N-qubit input states, are validated by test runs performed on a real quantum processor.
AbstractThe origin of the arrow of time—why entropy always increases, why we can only remember the past—is one of the deepest puzzles in physics. Boltzmann’s statistical explanation attributes entropy increase to a low-entropy “past hypothesis,” but it does not explain the origin of this initial condition itself. Landauer’s principle reveals a quantitative connection between information erasure and heat dissipation, yet it does not answer why information erasure is fundamentally irreversible. This paper proposes a unified solution within the two-phase information conservation framework: the arrow of time is the macroscopic statistical manifestation of the irreversibility of information settlement between the material phase (Ξ) and the information phase (Ω). Each information settlement event simultaneously produces four outcomes: formation of an information record, local collapse of the material phase state, update of observer coherence parameters, and consumption of dark energy accompanied by heat release. Once settlement is completed, it cannot be undone; the unidirectional flow of time is precisely the macroscopic bookkeeping of this settlement irreversibility. Starting from the principle of least action incorporating two-phase coupling, we provide a rigorous proof that the settlement process is not invariant under time reversal, and derive a quantitative relation between the entropy production rate and the macroscopic information activity rate. This framework unifies the thermodynamic arrow, the quantum measurement arrow, the decoherence arrow, and the cosmological arrow as manifestations of the same settlement process at different scales, offering a natural explanation for the past hypothesis and the entanglement past hypothesis. We present three testable predictions: a weak dependence of the CHSH violation parameter on the measurement time difference in Bell experiments, a scaling relation between decoherence rate and information-phase coupling strength at ultra-low temperatures, and the gravitational memory effect as a cumulative signature of settlement records on cosmological scales. This work unifies the arrow of time with quantum measurement, black hole information processing, dark energy cosmology, quantum entanglement, the Higgs mechanism, and the third law of thermodynamics under a single cross-scale information settlement paradigm.Keywords: arrow of time, second law of thermodynamics, Landauer’s principle, information settlement, irreversibility, entropy increase, time-reversal symmetry breaking, gravitational memory effect, past hypothesis
CosmoBeating • Absolute Zero (CB•AZ) From Quantum Randomness to Residual Activity This is a short, non-technical companion to the 6-paper CB•AZ series (Papers 0 to V). It is written for readers in physics, quantum thermodynamics, or philosophy of science, not for readers already familiar with the author’s wider framework. The core idea, stated plainlyAbsolute zero cannot be reached with finite resources and has not been observed as a naturally formed and maintained region in this universe. Within an information-realist premise—that information is not destroyed—the series treats this fact as a thermodynamic counterpart of the difficulty of completely extinguishing informational correlations. Residual activity and system–environment correlations are proposed as a bridging hypothesis. The claim is not that absolute zero is forbidden, but that it does not naturally appear. Only operational propositions are tested; ontological statements remain interpretive. Why the topic keeps returningThe third law, zero-point energy, and the question of whether information can reach zero appear in separate literatures: quantum refrigerators, vacuum structure, holographic encoding, and heat-death imagery. The series argues that many tensions arise from treating absolute zero as a possible final state of complete silence rather than as an asymptotic limit set by residual correlations. It keeps the operational floor (parasitic heating) separate from the additional residual-correlation term. Two layers kept apartOperational layer: cooling rate, residual heating, and measurable cross-correlation. These can be tested.Ontological layer: information as basis, fields as shadows. These are not confirmed or refuted by experiment. The series marks the distinction explicitly and does not claim priority over standard physics. What the series doesIt reframes quantum randomness as relative to an internal observer and information boundaries (Paper I), upgrades Einstein’s constraint after Bell to correlation structure (Paper II), treats measurement as redistribution rather than loss of active information (Paper III), locates residual activity at absolute zero and fields as shadows (Paper IV), and operationalises the bridging hypothesis as a temperature-floor relation with a residual-correlation term (Paper V, H1-F). What the series does not doIt does not alter the Born rule, add new dynamics, select among quantum interpretations, claim that absolute zero is physically forbidden, or assert that residual correlation has been experimentally confirmed. The residual-correlation term in H1-F is an internal conjecture. If it reduces to known heating, the operational claim is restricted. Ontological statements lie outside the scope of testing. What the series coversPaper 0: why absolute zero—motivation, position, series architecturePaper I: from quantum randomness to information boundariesPaper II: constraints of the unknowable and correlation ontologyPaper III: activity, inactivity, and the redistribution of informationPaper IV: absolute zero, zero-point activity, and the shadow status of fieldsPaper V: testable propositions—a temperature-floor relation with a residual-correlation term A note on methodEach paper separates standard published results, original proposals, and interpretive statements, and states its own failure or fallback conditions. Readers are encouraged to treat the operational proposals as falsifiable hypotheses, not as settled fact. Keywords: absolute zero, third law of thermodynamics, residual correlation, information realism, zero-point energy, heat death, quantum thermodynamics, CosmoBeating, information ontology AuthorWai-Hung Tam (Pan), Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com
Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, which states that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilized? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity. However, such optimal protocols require complex unitaries generated by an external work source. Restricting to unitaries that can be run solely via a heat engine, we derive a novel Carnot-Landauer limit, along with protocols for its saturation. This generalizes Landauer's principle to a fully thermodynamic setting, leading to a unification with the third law and emphasizes the importance of control in quantum thermodynamics.
CosmoBeating • Absolute Zero (CB•AZ) From Quantum Randomness to Residual Activity This is a short, non-technical companion to the 6-paper CB•AZ series (Papers 0 to V). It is written for readers in physics, quantum thermodynamics, or philosophy of science, not for readers already familiar with the author’s wider framework. The core idea, stated plainlyAbsolute zero cannot be reached with finite resources and has not been observed as a naturally formed and maintained region in this universe. Within an information-realist premise—that information is not destroyed—the series treats this fact as a thermodynamic counterpart of the difficulty of completely extinguishing informational correlations. Residual activity and system–environment correlations are proposed as a bridging hypothesis. The claim is not that absolute zero is forbidden, but that it does not naturally appear. Only operational propositions are tested; ontological statements remain interpretive. Why the topic keeps returningThe third law, zero-point energy, and the question of whether information can reach zero appear in separate literatures: quantum refrigerators, vacuum structure, holographic encoding, and heat-death imagery. The series argues that many tensions arise from treating absolute zero as a possible final state of complete silence rather than as an asymptotic limit set by residual correlations. It keeps the operational floor (parasitic heating) separate from the additional residual-correlation term. Two layers kept apartOperational layer: cooling rate, residual heating, and measurable cross-correlation. These can be tested.Ontological layer: information as basis, fields as shadows. These are not confirmed or refuted by experiment. The series marks the distinction explicitly and does not claim priority over standard physics. What the series doesIt reframes quantum randomness as relative to an internal observer and information boundaries (Paper I), upgrades Einstein’s constraint after Bell to correlation structure (Paper II), treats measurement as redistribution rather than loss of active information (Paper III), locates residual activity at absolute zero and fields as shadows (Paper IV), and operationalises the bridging hypothesis as a temperature-floor relation with a residual-correlation term (Paper V, H1-F). What the series does not doIt does not alter the Born rule, add new dynamics, select among quantum interpretations, claim that absolute zero is physically forbidden, or assert that residual correlation has been experimentally confirmed. The residual-correlation term in H1-F is an internal conjecture. If it reduces to known heating, the operational claim is restricted. Ontological statements lie outside the scope of testing. What the series coversPaper 0: why absolute zero—motivation, position, series architecturePaper I: from quantum randomness to information boundariesPaper II: constraints of the unknowable and correlation ontologyPaper III: activity, inactivity, and the redistribution of informationPaper IV: absolute zero, zero-point activity, and the shadow status of fieldsPaper V: testable propositions—a temperature-floor relation with a residual-correlation term A note on methodEach paper separates standard published results, original proposals, and interpretive statements, and states its own failure or fallback conditions. Readers are encouraged to treat the operational proposals as falsifiable hypotheses, not as settled fact. Keywords: absolute zero, third law of thermodynamics, residual correlation, information realism, zero-point energy, heat death, quantum thermodynamics, CosmoBeating, information ontology AuthorWai-Hung Tam (Pan), Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com
Absolute zero is usually introduced as a distinguished point of the Kelvin temperature scale, associated with the ground state of a system and the unattainability principle of the third law of thermodynamics. In conventional presentations this status is partly definitional and partly empirical. In this paper we derive the distinguished role of absolute zero from the first principles of the PAC–µ 8 framework, without additional empirical postulates. PAC–µ 8 is built on two structural ingredients: (i) a positive self-adjoint generator K≥ 0 with spectral bridge H = ℏ √ K, and (ii) a resource-cone inequality bounding coherent processes by four budget functionals ∆Sstop, ∥F∥ ⊗ , Wgate, Ttop under admissible boundary routing. We show that: (1) the positivity of K and the maximum-entropy construction together enforce a natural restriction to T ≥ 0 for equilibrium states; (2) the zero-temperature limit arises as a boundary point where the energy approaches the ground-state value and the stopping entropy budget saturates a minimal bound; and (3) under mild consistency assumptions (CSS conditions), absolute zero is unattainable by any finite-budget process, appearing only as a cone boundary limit of admissible transformations. We formulate absolute zero as the unique interface where (a) the equilibrium Gibbs family collapses onto the ground-state projector and (b) all thermodynamic evolution reduces to unitary rearrangements within the lowest spectral subspace, with no further decrease in resource-consistent entropy. The result clarifies that in PAC–µ 8 absolute zero is not an arbitrary convention and does not require new fundamental interactions; it is the inevitable boundary point of the resource cone generated by standard budgets over a positive generator.