The apparent contradiction between quantum mechanics and the second law of thermo?dynamics fundamentally stems from the opposition between dynamical reversibility andstatistical irreversibility. This paradox can be traced back to the classical debates sur?rounding Loschmidt’s paradox and Poincar´e’s recurrence theorem. Recent advancementsin quantum information theory have provided new tools to explore this issue. This frame?work proposes integrating fractal geometry with quantum dynamics to uncover intrinsicmechanisms of irreversibility within unitary evolution systems. The following outlines asystematically reconstructed research approach.
The apparent contradiction between quantum mechanics and the second law of thermo?dynamics fundamentally stems from the opposition between dynamical reversibility andstatistical irreversibility. This paradox can be traced back to the classical debates sur?rounding Loschmidt’s paradox and Poincar´e’s recurrence theorem. Recent advancementsin quantum information theory have provided new tools to explore this issue. This frame?work proposes integrating fractal geometry with quantum dynamics to uncover intrinsicmechanisms of irreversibility within unitary evolution systems. The following outlines asystematically reconstructed research approach.
Loschmidt's paradox asks why macroscopic irreversibility is universal despite the time-reversal symmetry of microscopic dynamics. We argue that irreversibility is not a property of the dynamics but of accessibility: chaotic evolution drives phase-space structure below the quantum resolution scale ℓℏ, at a critical time tc=λ−1ln(δ0/ℓℏ), after which the time-reversed microstate exists as a valid solution of Hamilton's equations but cannot be selected by any physically admissible operation. The mechanism operates entirely within the semiclassical regime tc≤tE, where classical geometry is exact. This provides a dynamical resolution of the Loschmidt paradox.
The quantum foundation is established using a Krylov-complexity framework: we prove that for any H(t)=H(−t), the quantum Lyapunov exponent satisfies λLforward=λLbackward. The arrow of time is not in the dynamics. The mechanism predicts sigmoid fidelity decay, logarithmic scaling of tc with λ−1, and ensemble-size independence of the inaccessibility threshold -- all consistent with three decades of Loschmidt echo experiments and confirmed in a stadium-billiard simulation reported here. Underlying everything: quantum mechanics conserves information exactly. Entropy, defined as the logarithm of the multiplicity Ω -- the number of possibilities consistent with the available information -- can only increase when information becomes operationally inaccessible. The second law reflects not a breakdown of microscopic reversibility, but the dynamical inaccessibility of the information required to reverse it.
The fundamental laws of classical mechanics, quantum mechanics, and general relativity are time-symmetric, yet macroscopic experience is irreversible without exception. Standard physics bridges this gap with statistical argument: reversal is treated as merely improbable, not physically inadmissible. This paper argues that the gap is an artifact of treating space as a continuum, and that it closes once space is treated as discrete, as in Quantum-Geometry Dynamics (QGD). Two independent grounds are identified for the categorical, non-statistical irreversibility of every elementary interaction in discrete space: a local ground, the loss of individual addressability when one particle's constituent preon(+)s merge into another upon absorption; and a global ground, the irreducible universal gravitational trace left by any positional change, given that gravity in QGD is instantaneous and universal in scope. Applied across four domains, this single result dissolves the arrow-of-time problem, grounds the second law of thermodynamics in dynamics rather than probability, dissolves the apparent asymmetry between unitary evolution and measurement collapse, and shows the reversible/irreversible distinction in quantum gate theory to be a feature of the abstract computational model rather than of physical mechanism. The result is shown to be compatible with, and silent on, whether a finite deterministic system's forward dynamics eventually revisit an earlier configuration by a non-retracing causal path. No new axiom or free parameter is introduced: the result follows from elements of QGD already established for independent reasons.
This report constructs a rigorous theoretical bridge connecting the deterministic evolution of isolated quantum systems, governed by the Hamiltonian operator, with the irreversible, macroscopic thermalization demanded by the second law of thermodynamics. It utilizes the Eigenstate Thermalization Hypothesis (ETH) to reconcile this contradiction, asserting that individual energy eigenstates are intrinsically thermal. To transcend ETH's descriptive limits, the Statistical Jacobi Approximation (SJA) is introduced to predict far-from-equilibrium dynamics and response functions following quantum quenches without requiring complete re-diagonalization. The document demonstrates that multiscale energy transfer, specifically the inverse energy cascade mediated by recursive zig-zag patterns observed in classical turbulence, persists within microscopic quantum superfluids and optical lattices. Critically, to stress-test these frameworks, the report employs fractal geometries as advanced simulational incubators. Fractals, by Mamun, SM (2026) ………………………….1 Quantum Mechanics, the Hamiltonian, and Thermodynamics: Predicting Eigenstates via Fractal Simulations (Volume II) K S C breaking translational symmetry, lead to the emergence of non-ergodic multifractal (NEM) states that actively defy ETH, and provide empirical validation through the high-resolution observation of Hofstadter's Butterfly in moiré superlattices. Also available on Academia.edu: https://www.academia.edu/attachments/132683179/download_file?s=portfolio
The contradiction between the unitarity of quantum mechanics and the irre?versibility of thermodynamics is one of the core challenges in modern physics. Tra?ditional statistical mechanics explains macroscopic disorder and entropy increasethrough the concept of entropy but fails to uncover its geometric essence. This pa?per proposes the Dynamic Rigid Fractal Theory, redefining the geometric propertiesof the wavefunction, the physical meaning of entropy increase, and the quantum-to?classical transition mechanism from the perspective of dynamic fractal geometricevolution. By introducing the dynamic fractal dimension Df (t) and the fractaltension field Tf (x, t), the geometric attributes of the wavefunction are redefined,the dynamic evolution equation of fractal dimensions is derived, and the underly?ing geometric laws of entropy increase are revealed in conjunction with the physicalphenomena of decoherence and measurement. This paper further demonstrates howthe theory aligns with the traditional definitions of entropy in statistical mechanics(e.g., Boltzmann entropy) while extending the geometric interpretation of entropy.Ultimately, the Dynamic Rigid Fractal Theory not only resolves the core contradic?tion between quantum mechanics and thermodynamics but also provides a deeperexplanation for entropy increase and proposes specific experimental predictions tovalidate its key results.
The discussion on time-reversal in quantum mechanics exists at least since Wigner's ``Uber die Operation der Zeitumkehr in der Quantenmechanik'' paper in 1932. If and how the dynamics of the quantum world is time-reversible has been the subject of many controversies. Some have seen quantum mechanics as fundamentally time-irreversible, see for example von Neumann, and some have seen in that the ultimate cause of time's arrow and second law behavior. In his best-selling book ``The Emperor's New Mind'', Roger Penrose argues similarly and concludes that ``our sought-for quantum gravity must be a time-asymmetric theory'' [p.351]. Not so long ago, we read yet about another project in Physicalia 26: to extend quantum mechanics into new fundamentally irreversible equations, thus proposing a new theory giving ``... une description fondamentale irreversible de tout systeme physique''.