Art Collection Management Software represents a distillation of the seemingly arcane, yet intellectually stimulating, world of art collection into a technological framework. It is an interactive, analytical, and dynamic system that provides a solution to the multitude of challenges inherent in managing an art collection.

Conceptually, an Art Collection Management Software (ACMS) is a digital system designed to facilitate the storage, organization, and retrieval of information related to an art collection. It is primarily aimed at art collectors, museums, galleries, and other institutions that house large collections of artworks. This software, at its core, is an amalgamation of diverse fields such as history, economics, statistics, law, and information technology - each playing a crucial role in its design and functioning.

From a historical perspective, ACMS is a by-product of the transition of art collection management from traditional methods to more sophisticated and technologically advanced ones. Traditionally, art collection management was a labor-intensive process, often requiring physical documentation, tracking, and archiving. However, with the advent of digital technology, and its subsequent permeation into numerous industries, a paradigm shift occurred.

In the realm of economics, the ACMS is not merely a tool for convenience but also a strategic investment. The cost of implementing such software is often offset by the potential economic benefits it brings about. These include increased efficiency, reduced risk of loss or damage, enhanced security, and potential for high ROI in terms of sales and valuation of art pieces.

Statistically speaking, an ACMS offers a more robust and reliable method of tracking and analyzing data related to an art collection. The software provides tools for accurate data entry, efficient data management, and sophisticated data analysis. This goes beyond mere numbers and extends to the analysis of trends, patterns, and correlations – invaluable assets for any serious art collector or institution.

From a legal standpoint, an ACMS facilitates compliance with various local and international laws related to art collection. It helps in maintaining a clear and accurate record of the provenance and authenticity of artworks, which are critical in dispute resolution and in establishing ownership.

At the heart of an ACMS is an intricate web of information technology tools and concepts. Database management systems provide the backbone for storage and retrieval of data, while user interface (UI) design elements ensure the software is easy to use and navigate. On the other hand, concepts like cloud computing and encryption bring about the much-desired mobility and security to the system.

The functionality of an ACMS is built around the central idea of providing a comprehensive solution to all the possible challenges in art collection management. This includes inventory management, condition reporting, loan tracking, exhibition planning, shipping and logistics, insurance, and even sales and client management. The software thus serves as a multi-faceted, one-stop solution for all the needs of an art collector or institution.

Despite the benefits, one must also be mindful of the potential drawbacks and challenges. There can be a steep learning curve associated with the software, especially for those not well-versed in technology. Data privacy and security is another concern due to the sensitive nature of the information involved. Therefore, it is essential to choose a software that prioritizes data protection and has robust security measures in place.

In conclusion, Art Collection Management Software represents the confluence of art and technology – a testament to the evolution of art collection management. It is an exciting frontier, offering an innovative, efficient, and interactive method of managing art collections. Although not without its challenges, the benefits and potential it offers make it an indispensable tool in the modern world of art collection.