Generative Large Language Models (LLMs) stand as a revolutionary advancement in the modern era of artificial intelligence (AI). However, directly deploying LLMs in resource-constrained hardware, such as Internet-of-Things (IoT) devices, is difficult due to their high computational cost. In this paper, we propose a novel information-entropy framework for designing mobile-friendly generative language models. Our key design paradigm is to maximize the entropy of transformer decoders within the given computational budgets. The whole design procedure involves solving a mathematical programming (MP) problem, which can be done on the CPU within minutes, making it nearly zero-cost. We evaluate our designed models, termed MeRino, across nine NLP downstream tasks, showing their competitive performance against the state-of-the-art autoregressive transformer models under the mobile setting. Notably, MeRino achieves similar or better zero performance compared to the 350M parameter OPT while being 4.9x faster on NVIDIA Jetson Nano with 5.5x reduction in model size. Code will be made available soon.