If an apartment complex has a no smoking rule and says "you cannot smoke on our property, including the public side walks surrounding the building or you will be fined" How can they enforce that against members of the public who smoke in public? Can they enforce it against tenants if it is part of the lease agreement?
There is no public property on private land; there is private property where the public has implicit permission to be for legitimate purposes - shoppers in a shopping mall, visitors and residents in an apartment complex etc.
That permission can be revoked subject to any contractural (e.g. tenants) or statutory obligations (e.g. access for emergency services) at any time for any or no reason. For example, if the complex has a no smoking rule and a person persists in smoking after they can be asked to leave; if they don't leave, they are committing the tort and the crime of trespass.
Now, in common law jurisdictions, only governments have the right to impose punishment for offences; a fine is a punishment so an owner's corporation cannot impose one on anyone. They can sue for damages for torts or breach of contract but only to the extent of the damage caused (except in the US where punitive damages are a thing); so whatever damage the smoking/trespass caused; probably not much. Parties to a contract can agree on an amount of liquidated damages but to be enforceable they must be a genuine pre-estimate of the costs incurred by the breach; if they are too large they are a penalty clause and penalty clauses are unenforceable.
They can't. Maybe.