A molecular switch flips between a closed state and an open state with constant…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Non-equilibrium statistical mechanics and stochastic thermodynamics · Non-equilibrium statistical mechanics and stochastic thermodynamics

Error, Chance and the Machine, Ch Random processes in continuous time

Problem

A molecular switch flips between a closed state

C

and an open state

O

with constant rates: opening rate

300\,\mathrm{s^{-1}}

(from

C

O

) and closing rate

700\,\mathrm{s^{-1}}

(from

O

C

). ((a)) Write the master equation for the open probability

p_O(t)

and find the equilibrium open fraction. ((b)) Find the relaxation time constant of the approach to equilibrium.

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