Quantum Inaccessibility

TL;DR

This paper proposes a dynamical explanation for macroscopic irreversibility, showing that quantum inaccessibility arises from chaotic evolution and phase-space structure below quantum resolution, resolving Loschmidt's paradox.

Contribution

It introduces a mechanism within semiclassical dynamics explaining irreversibility without breaking microscopic reversibility, supported by theoretical proof and numerical simulations.

Findings

Sigmoid fidelity decay observed in experiments and simulations.

Logarithmic scaling of critical time with Lyapunov exponent.

Inaccessibility threshold is independent of ensemble size.

Abstract

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 $t_c = \lambda^{-1}\ln(\delta_0/\ell_\hbar)$, 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 $\lambda_L^{\rm forward} = \lambda_L^{\rm backward}$. The arrow of time is not in the dynamics. The mechanism predicts sigmoid fidelity decay, logarithmic scaling of $t_c$ with $\lambda^{-1}$, 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 $\Omega$ -- 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.