Productivity management software has been a game-changer in businesses, large and small, establishing its importance in optimizing workflow and enhancing efficiency. As we move forward into the technological future, this sector is far from stagnation. Today, we shall discuss the future predictions and emerging trends that are set to revolutionize this industry.

The driving force behind the evolution of productivity management software is the ever-increasing demand for efficiency and productivity in our workplaces. The push for more efficient business operations, combined with the rapid technological advancements, is reshaping the landscape, leading us to a future more reliant on software for productivity management.

One key prediction is the increased integration of artificial intelligence (AI) and machine learning (ML) into the core of productivity management software. Already, we see AI’s fingerprints on various management applications that leverage natural language processing to sort and respond to emails, or use machine learning to automate repetitive tasks.

AI and ML, in essence, provide the ability for software to learn from its experiences, adapt to new inputs, and perform human-like tasks. In the context of productivity management, they can be utilized to automate routine tasks, enhance decision making, and provide insights from large data sets - all contributing to increased productivity.

However, it is noteworthy that such AI integration might not be universally beneficial. AI systems need substantial data to function effectively, which may raise privacy concerns. Moreover, over-reliance on AI could reduce human jobs, leading to social and economic issues. Thus, a fine balance needs to be struck between AI utilization for productivity and the preservation of human roles and privacy.

Another emerging trend is the rise of mobile productivity applications. As the digital world moves from desktop to mobile, productivity software is following suit. Future productivity software systems are predicted to make greater use of mobile platforms, employing mobile-first or mobile-only strategies. This shift towards mobility is due to the increasing trend of remote working and the need to manage productivity on-the-go.

Asynchronous communication is another area predicted to shape the future of productivity management software. This type of communication allows team members to contribute at their own pace without interrupting others. It is being increasingly incorporated into productivity software, primarily to cater to geographically dispersed teams operating in different time zones – a common scenario in today’s globalized business environment.

There are tradeoffs to consider with asynchronous communication as well. While it can boost productivity by reducing interruptions during focused work, it can also lead to communication delays and potential misunderstandings if not managed correctly.

The future of productivity management software may also see a greater emphasis on personalization. With businesses becoming more diverse in terms of their requirements and workflows, there is a growing demand for software that is not 'one-size-fits-all'. Hence, it is predicted that there will be a rise in productivity software that can be tailor-made according to the needs and nature of the business.

To conclude, these are predictions based on current trends and are subject to change with the dynamic nature of technology and business environments. The future of productivity management software is promising, with possibilities for more significant integration of artificial intelligence, mobile-first strategies, asynchronous communication, and personalization, among others. Yet, a thoughtful approach is required to navigate the possible pitfalls of over-reliance on technology and ensure a future where productivity software continues to be a tool that aids human effort, rather than replacing it.