Classical thermodynamics describes temperature, pressure and entropy as bulk, macroscopic properties of a system, established through direct measurement without needing to reference what's actually happening at the level of individual particles. Statistical thermodynamics takes a genuinely different approach to the exact same underlying physical reality: it derives those same familiar bulk properties from the statistical behaviour of the enormous numbers of individual atoms or molecules a system is actually made of, explaining why the classical thermodynamic laws hold by counting microscopic possibilities rather than treating heat and temperature as self-contained macroscopic quantities in their own right.
A system's macroscopic state corresponds to a huge number of microscopic arrangements
Any given macroscopic state of a system, a particular temperature and volume of gas, for instance, can actually be realised by an enormous number of different specific microscopic arrangements of its individual particles' positions and velocities. Statistical thermodynamics treats a system's observed macroscopic properties as reflecting the statistical average behaviour across this vast number of microscopically distinct but macroscopically equivalent arrangements, rather than corresponding to any single, specific microscopic configuration. Temperature, in this framework, emerges as a statistical measure directly related to the average kinetic energy across a system's particles, not as some separate, independently existing physical substance.
Entropy counts how many microscopic arrangements produce the same macroscopic outcome
Entropy receives a particularly clarifying reinterpretation under statistical thermodynamics: rather than being defined only abstractly through heat flow, as in classical thermodynamics, entropy can be understood directly as related to the number of distinct microscopic arrangements consistent with a given macroscopic state, with a higher entropy state corresponding to a state achievable through a much larger number of possible microscopic arrangements. This statistical reframing explains why entropy tends to increase in an isolated system: a system evolving toward states reachable through more possible microscopic arrangements is, statistically, simply far more likely to end up there than in a comparatively rare, highly ordered low-entropy state, without needing any additional physical law beyond basic probability.
What we're still unsure about
The basic statistical-mechanical derivation of temperature and entropy from microscopic particle behaviour is well established, foundational physical chemistry, extensively confirmed across a huge range of experimentally studied systems. What remains more genuinely an active area of ongoing research is extending statistical thermodynamics' methods to systems that are far from equilibrium, or that involve strong, complicated interactions between particles, since the cleanest statistical results generally rely on assumptions, like particles being independent or a system sitting near equilibrium, that don't always hold for more complex real systems — researchers continue actively developing statistical approaches for these more difficult, interaction-heavy cases, without a single universally applicable framework that already covers every such situation cleanly.
This sits inside Statistical Thermodynamics, one of seven topics in Physical Chemistry, one of six domains in Chemistry, one of seventeen subjects the app can quiz you on.