by A. May, Aug 9, 2026 in WUWT
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Local temperature
This is the temperature used in climate and meteorological studies. It is the foundation of heat conduction, and hydrodynamics. One assumes local thermodynamic equilibrium over some volume and measures or assumes a local temperature for the volume. This is the logic used in the famous Navier-Stokes equations. This assumed “local equilibrium” is valid over small volumes (for example an “air parcel”) for short time periods. The problem with some climate models is that they assume “local equilibrium” for volumes and time periods that are too large and too long.
Discussion
Temperature is not a primitive mechanical property like mass; it is an emergent statistical property that characterizes the distribution of energy among degrees of freedom (Landau & Lifshitz, 1980). Mass can be measured independently of the rest of the universe or system and does not change as the system around it changes. Temperature follows from the 0th law of thermodynamics, which says:
If system A is in thermal equilibrium with system B,
and system B is in thermal equilibrium with system C,
then A is in thermal equilibrium with C.
The 0th law establishes that “temperature” is a meaningful physical quantity because thermal equilibrium is transitive. It does not define temperature, but it guarantees that temperature is meaningful and measurable. We often hear that temperature is transitive, but this is only true in laboratory settings or at equilibrium. Outside equilibrium, temperature can lose transitivity and different degrees of freedom can produce different temperatures. Transitivity is the basis of equilibrium temperature, but not all temperature measurements.
In summary, the thermodynamic definition of temperature applies only to equilibrium states, but physics uses many other temperature concepts like kinetic, effective, local, and generalized that are essential for describing real systems far from equilibrium. Restricting “temperature” to its equilibrium definition ignores the vast range of physical systems where temperature is well-defined and indispensable.
