Rather than "do nothing" if there is nothing to do (including SMP), why linux kernel runs idle thread?
When the scheduler decides to switch to the idle task, at this point, the dynamic tick begins to work, by disabling periodic tick until the next timer expires. The tick will be reenabled after this time span or when an interrupt occurs at some time.
In the mean time, the CPU is going to a well-deserved sleep, in an architecture-specific way, therefore saving your power. Take a look at the definition of cpu_idle() in arch/x86/kernel/process.c.
/*
* The idle thread. There's no useful work to be
* done, so just try to conserve power and have a
* low exit latency (ie sit in a loop waiting for
* somebody to say that they'd like to reschedule)
*/
void cpu_idle(void)