Resilience of parity-violation-induced chiral selectivity to nonequilibrium temperature fluctuations in open systems

Abstract

We consider the sensitivity of chemical reactions, able to undergo spontaneous mirror symmetry breaking, to chiral bias in the presence of nonequilibrium temperature fluctuations and derive a selectivity criterion. For this, we estimate the magnitude of fluctuations $\ensuremath{\delta}k$ in chemical reaction rate constants $k$ arising from the nonequilibrium temperature fluctuations $\ensuremath{\delta}T$ about a mean value $T$. To leading order, the relative rate constant fluctuations $\ensuremath{\delta}{k}_{i}/{k}_{i}$ for each reaction $i$ are given by the product of the activation enthalpy $\mathrm{\ensuremath{\Delta}}{H}_{i}^{\ifmmode\ddagger\else\textdaggerdbl\fi{}}/RT$ for the $i\mathrm{th}$ reaction multiplied by the relative rms temperature fluctuations $\ensuremath{\delta}{T}_{\mathrm{rms}}/T$. The latter are determined by the system's specific heat at constant volume: ${C}_{V}$. We test this criterion with simulations carried out for an open-flow fully reversible Frank model, and for a range of parity-violating energy differences (PVED) within the theoretically estimated upper and lower bounds. Depending on the relative magnitudes of the deterministic PVED bias and the temperature fluctuations, the PVED bias can either (i) select the final stable chiral outcome deterministically or (ii) select one of two possible stable chiral outcomes with an asymmetric statistical weighting. For larger temperature fluctuations, the PVED bias loses its selectivity, and the final stable chiral outcomes are stochastic and equally probable. This paper points towards the possible design of small volume chemical flow reactors capable of detecting the elusive PVED bias in bulk systems, provided other sources of fluctuations can be sufficiently controlled and attenuated.