In this work, we present a novel unified equation of state (UEOS) that integrates thermodynamic variables across all phases of matter, challenging longstanding paradigms in quantum mechanics and statistical physics. By deriving the UEOS from first principles combining relativistic invariance and nonlocal field interactions, we demonstrate that particle-wave duality emerges as an artifact of incomplete classical approximations rather than a fundamental property of quantum systems. Our analysis reveals those apparent dual behaviors in phenomena such as the double-slit experiment stem from emergent statistical fluctuations in the UEOS, effectively debunking the need for intrinsic duality and reconciling quantum observations with a purely field-theoretic framework. Furthermore, entropy is reinterpreted not as a measure of disorder but as a pseudo-thermodynamic quantity arising from incomplete knowledge of the UEOS parameters, resolving paradoxes in information theory and black hole thermodynamics. Finally, the UEOS elucidates the mystery of phase transitions by providing a continuous analytic function that predicts critical points without invoking symmetry breaking or renormalization group flows, offering exact solutions for van der Waals-like behaviors in real gases and superconductors. This unified approach not only simplifies the theoretical landscape but also suggests experimental tests via high-precision calorimetry and interferometry, paving the way for a paradigm shift in foundational physics.
Macro-orbital representation of a particle (detailed account given in cond-mat/0603784) has been used to develop the microscopic theory of a system of interacting bosons. It concludes that: (i) below certain temperature (say,
Tλ), particles assume a state of (q, -q) bound pairs, (ii) the
λ−transition is a consequence of inter-particle quantum correlations clubbed with zero-point repulsion and inter-particle attraction and represents an onset of the order-disorder of particles in their
ϕ−space followed simultaneously by their BEC as (q, -q) bound pairs in a state of q =
qo=π/d and K = 0, (iii) particles at
T≤Tλ acquire collective binding which locks them at = 0, =
λ/2 and
Δϕ=2nπ (with n = 1, 2, 3, ...), (iv) the entire system assumes mechanical strain in inter-particle bonds and behaves like a single macroscopic molecule, (v) there exists an energy gap between the superfluid and normal fluid phases of the system, (vi) the
λ−transition represents the twin phenomena of broken gauge symmetry and phase coherence, (vii) the system does not have p = 0 condensate, (viii) a new kind of quantum quasi-particle "omon" (a phononlike wave of the oscillations of the momentum coordinates of particles) exists in superfluid phase, etc. It explains the properties of He-II, including the origin of quantized vortices, critical velocities, logarithmic singularity of specific heat, etc. at quantitative level and provides microscopic foundation to two fluid theory,
Ψ−theory, idea of macroscopic wave function, etc. The framework of the theory can unify the physics of interacting bosons and fermions.
We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.
We show that universal properties of a many-atom quantum system exist at a much higher density, or a much shorter length scale, than those implied by traditional theories for a dilute Bose gas. In particular, a universal equation of state at length scale β6 = (mC6/2)1/4 (corresponding to the van der Waals interaction) is defined and investigated by combining the concept of effective potential, the constrained variational method and the analytic solution for the van der Waals potential. In one application, we show that a many-atom Bose system with negative scattering length may form a metastable liquid Bose–Einstein condensate (BEC) state with an equilibrium density that is controlled by a scaled scattering length.
We show that universal properties of a many-atom quantum system exist at a much higher density, or a much shorter length scale, than those implied by traditional theories for a dilute Bose gas. In particular, a universal equation of state at length scale β 6 = ( mC 6 /ℏ 2 ) 1/4 (corresponding to the van der Waals interaction) is defined and investigated by combining the concept of effective potential, the constrained variational method and the analytic solution for the van der Waals potential. In one application, we show that a many-atom Bose system with negative scattering length may form a metastable liquid Bose–Einstein condensate (BEC) state with an equilibrium density that is controlled by a scaled scattering length.
Abstract In this chapter, the singular changes accompanying a phase transition requires the existence of macroscopic correlations. As a consequence, phase transitions mark a stark departure from the noninteracting and linear responding systems we have considered thus far. Understanding phase transi- tions requires that we study strongly interacting models, pushed far into regimes of nonlinear response. This complication renders detailed studies largely intractable analytically. However, some simplifications exist that allow for a general theory of phase transitions to be developed. These are the notions of universality that accompany phase transition phenomenology, and the ability to classify phase transi- tions simply using ideas of spontaneous symmetry breaking. The former allows us to postulate simple models bereft for molecular detail and yet still provide quantitative predictions for observable behavior. The latter allows us to predict what phases can exist, and understand why phase transitions occur.