Quantum Inaccessibility
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908950053519360 |
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| author | Wolfson, Ira |
| author_facet | Wolfson, Ira |
| contents | 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 $\ell_\hbar$, at a critical time $t_c = λ^{-1}\ln(δ_0/\ell_\hbar)$, 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 $t_c \leq t_E$, 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 $λ_L^{\rm forward} = λ_L^{\rm backward}$. The arrow of time is not in the dynamics. The mechanism predicts sigmoid fidelity decay, logarithmic scaling of $t_c$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Inaccessibility Wolfson, Ira Statistical Mechanics Chaotic Dynamics History and Philosophy of Physics Quantum Physics 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 $\ell_\hbar$, at a critical time $t_c = λ^{-1}\ln(δ_0/\ell_\hbar)$, 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 $t_c \leq t_E$, 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 $λ_L^{\rm forward} = λ_L^{\rm backward}$. The arrow of time is not in the dynamics. The mechanism predicts sigmoid fidelity decay, logarithmic scaling of $t_c$ 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. |
| title | Quantum Inaccessibility |
| topic | Statistical Mechanics Chaotic Dynamics History and Philosophy of Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.03843 |