Experimental data and the principles of quantum mechanics suggest that a crystal is a condensate of `wavicles' enclosed in a box, where `wavicle' denotes the indefinite wave-particle status of the microscopic constituents. When it is not perturbed the crystal is in a classical-like state. The wavefunction, the internal energy and the entropy are all of them equal to zero. The thermodynamic temperature is indefinite. Perturbations via energy- and/or momentum-transfer reveal quantum effects. The temperature laws for the heat capacities of some hydrogen-bonded crystals are rationalized with superposition states depending on the quantum temperature which is crystal-dependent. Heat-transfer is a coherent anentropic process. Apart from energy conservation, the other laws of thermodynamics are irrelevant.
Experimental data and the principles of quantum mechanics suggest that a crystal is a condensate of wavicles' enclosed in a box, where wavicle' denotes the indefinite wave-particle status of the microscopic constituents. When it is not perturbed the crystal is in a classical-like state. The wavefunction, the internal energy and the entropy are all of them equal to zero. The thermodynamic temperature is indefinite. Perturbations via energy- and/or momentum-transfer reveal quantum effects. The temperature laws for the heat capacities of some hydrogen-bonded crystals are rationalized with superposition states depending on the quantum temperature which is crystal-dependent. Heat-transfer is a coherent anentropic process. Apart from energy conservation, the other laws of thermodynamics are irrelevant.
Introduction In most of the discussion presented so far in this book, the quantum character of atoms and electrons has been ignored. The Ising spin models have been an exception, but since the Ising Hamiltonian is diagonal (in the absence of a transverse magnetic field), all energy eigenvalues are known and the Monte Carlo sampling can be carried out just as in the case of classical statistical mechanics. Furthermore, the physical properties are in accord with the third law of thermodynamics for Ising-type Hamiltonians (e.g. entropy S and specific heat vanish for temperature T → 0, etc.) in contrast to the other truly classical models dealt with in previous chapters (e.g. classical Heisenberg spin models, classical fluids and solids, etc.) which have many unphysical low temperature properties. A case in point is a classical solid for which the specific heat follows the Dulong–Petit law, C = 3 Nk B , as T → 0, and the entropy has unphysical behavior since S → –∞. Also, thermal expansion coefficients tend to non-vanishing constants for T → 0 while the third law implies that they must be zero. While the position and momentum of a particle can be specified precisely in classical mechanics, and hence the groundstate of a solid is a perfectly rigid crystal lattice (motionless particles localized at the lattice points), in reality the Heisenberg uncertainty principle forbids such a perfect rigid crystal, even at T → 0, due to zero point motions which ‘smear out’ the particles over some region around these lattice points. This delocalization of quantum-mechanical particles increases as the atomic mass is reduced; therefore, these quantum effects are most pronounced for light atoms like hydrogen in metals, or liquid helium. Spectacular phenomena like superfluidity are a consequence of the quantum nature of the particles and have no classical counterpart at all. Even for heavier atoms, which do not show superfluidity because the fluid–solid transition intervenes before a transition from normal fluid to superfluid could occur, there are genuine effects of quantum nature. Examples include the isotope effects (remember that in classical statistical mechanics the kinetic energy part of the Boltzmann factor cancels out from all averages, and thus in thermal equilibrium no property depends explicitly on the mass of the particles).
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical mechanics. A self-consistent Hamiltonian has then been constructed for a given quantum many-body system which includes the effect of temperature in the form of correction terms added to the corresponding zero-temperature Hamiltonian of the system. Investigating some quantum mechanical systems with exact zero-temperature solutions including the particle-in-a-box model, the free particle, and the harmonic oscillator within our finite-temperature approach up to the first order of self-consistency has led to temperature-dependent Hamiltonians describing these systems above absolute zero without encountering any physically unacceptable brand of behavior for their wave functions and energy spectra. Results firmly support the view that a quantum mechanical system at a finite temperature behaves as if it is in a zero-temperature excited state.
Abstract Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the possible transformations of open quantum systems. The foremost quantum thermodynamic law is a simple statement concerning the conservation of energy. Nevertheless, there exist ambiguity and disagreement regarding the precise partition of a quantum system’s energy change to work and heat. By treating quantum mechanics as a comprehensive theory, applicable to both the micro and macroscopic domains, and employing dynamical symmetries, we bridge the gaps between five popular thermodynamic approaches to the first law. These include both autonomous and semi-classical formulations, which define work in terms of an ensemble average, as well as the single shot paradigm, where work is defined as a deterministic quantity.
A persistent conceptual puzzle in statistical mechanics is that the entropy S of a classical ideal gas depends on quantum mechanical quantities such as Planck's constant h and the factor 1/N!, which is commonly attributed to the indistinguishability of quantum particles. We resolve this puzzle by distinguishing entropy differences ΔS computed within the gas phase from those computed across a phase transition. For thermodynamic transformations within the gas phase, ΔS depends exclusively on classical macroscopic variables. In such processes, both h and 1/N! contribute only additive constants that cancel in ΔS, rendering them irrelevant for classical measurements. However, computing the latent heat released during a phase transition requires the entropy difference between two distinct phases with fundamentally different microscopic structures. Since the additive contributions do not cancel across phase transitions, a microscopic theory that correctly counts the states of each phase becomes essential, and quantum mechanics is required.
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