This paper presents an algorithm for adaptive cooperative exploration of a priori unknown environments using a team of unmanned systems (e.g., autonomous underwater vehicles (AUVs)). These systems are required to perform time-critical operations either with very limited human supervision or as fully autonomous entities. Typical operations include exploration, terrain-map generation, searching and rescuing targets from hazardous situations, cleaning of chemical spills, humanitarian de-mining (i.e., mine counter measures (MCM)), and detection of underwater mobile targets (i.e., anti-submarine warfares (ASW)). Furthermore, these unmanned systems have an a priori decided plan of action that is computed offline using multi-objective optimization methods. However, these optimization methods do not include uncertainties such as unknown objects (e.g., obstacles) and changing environment. Thus, these autonomous systems must be capable of adapting their navigation trajectories quickly as the knowledge of the environment changes. The new information is acquired in situ by onboard sensing. In this regard, this paper focuses on the problem of complete coverage of a priori unknown environments using a team of autonomous underwater vehicles and introduces a novel method based on the concepts of Statistical Mechanics. A key feature of this method is that the underlying algorithm relies on the notion of multiresolution navigation that consists of local and global navigation functions depending on the amount of spatiotemporal information needed for making the navigation decision. This feature supplies two potential advantages to the algorithm: i) the Local Navigation Potential (LNP) provides a reduced computational complexity in making real-time locally optimal navigation decisions via avoiding unnecessary global calculations and ii) the Global Navigation Potentials (GNPs), that are organized in a hierarchical manner, prevent the algorithm from getting stuck into a local extremum. The algorithm switches from the local to the global navigation and vice versa as needed. The autonomous systems share information with nearest neighbors for collaboration. This algorithm guarantees complete coverage of the search area and inherently prevents the problem of local minima that is commonly encountered in potential field based methods. The efficacy of the algorithm is validated on the high-fidelity Player/Stage simulator of mobile robots.