What authority does a court have to give supplemental jury instructions to a deadlocked jury in a criminal case?

"The trial court's authority to give supplemental jury instructions to a deadlocked jury in a criminal case derives from Penal Code section 1140, which provides, 'Except as provided by law, the jury cannot be discharged after the cause is submitted to them until they have agreed upon their verdict and rendered it in open court, . . . unless, at the expiration of such time as the court may deem proper, it satisfactorily appears that there is no reasonable probability that the jury can agree.'" (People v. Whaley (2007) 152 Cal.App.4th 968, 979.)

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"The determination, pursuant to section 1140, whether there is a '"reasonable probability"' of agreement, rests within the sound discretion of the trial court. [Citation.] Although the court must take care to exercise its power without coercing the jury into abdicating its independent judgment in favor of considerations of compromise and expediency [citation], the court may direct further deliberations upon its reasonable conclusion that such direction would be perceived '"as a means of enabling the jurors to enhance their understanding of the case rather than as mere pressure to reach a verdict on the basis of matters already discussed and considered." [Citation.]' [Citation.]" (People v. Proctor (1992) 4 Cal.4th 499, 539.)