Thermodynamic Constraints on the Continuity of Physical Space

The assumption that physical space is continuous plays a central role in modern theoretical physics, yet it lacks direct experimental support. In contrast, the laws of thermodynamics are empirically established and form one of the most reliable frameworks in physics. This paper examines a fundamental inconsistency between spatial continuity and the thermodynamic requirements of finite, countable microstates and non-zero entropy gradients. A continuous spatial manifold implies an unbounded microstate measure, rendering entropy ill-defined and undermining the Second and Third Laws. Conversely, the empirical validity of thermodynamics requires that physical state-space possess finite resolution and discrete partitions. By analyzing this tension without introducing model-dependent assumptions, we show that the continuity of space cannot be maintained alongside the established structure of thermodynamic law. The result is a general constraint on the ontology of physical space derived solely from experimentally verified principles.