The Time-Identity Tradeoff

Distinguishability plays a major role in quantum and statistical physics. When particles are identical their wave function must be either symmetric or antisymmetric under permutations the number of microscopic states, which determines entropy, is counted up to permutations. distinguishable, wavefunctions have no symmetry each permutation different microstate. This binary discontinuous classification raises few questions: one may wonder what happens if almost identical, when property that distinguishes between them irrelevant physical interactions given system. Here I sketch general answer these questions. For any pair non-identical there timescale, $\tau_d$, required for measurement resolve differences them. Below seem above it - different, uncertainty principle provides lower bound $\tau_d$. Thermal systems admit conjugate temperature scale, $T_d$. Above this system appears equilibrate before resolves particles, below identifies equilibration. As decline towards zero, $\tau_d \to \infty$ $T_d 0$.