The normal log level in production is info, so debug logs are not shown.
Change your logging to
Rails.logger.info "Year: #{Time.now.year}"
to show it in production.log.
Alternatively (but not a good idea) you can raise the logging level in /config/environments/production.rb:
config.log_level = :debug
Update Rails 4.2:
Now the default debug level in all environments is :debug (as @nabilh mentioned).
If you want you production environment less chattery, you can reset your log level in /config/environments/production.rb to the former :info:
config.log_level = :info