## Zeroth Law of Thermodynamics and Transitivity of Simultaneity

There are two important laws of transitivity in physics (Zhao, 1991).One is the zeroth law of thermodynamics, which states the transitivity of thermal equilibrium. The other is the law of the transitivity of simultaneity in general relativity (Landau and Lifshitz, 1975), which says that one can synchronize coordinate clocks placed along a closed path to a simultaneous moment if and only if the reference frame is time-orthogonal.In this paper, we will give a fundamental and intrinsic relationship between the two laws on transitivity in physics. The transitivity of thermal equilibrium is equivalent to the transitivity of clock rate synchronization.In Section 2 we show the relationship between the transitivity of thermal equilibrium and the transitivity of clock rate synchronization by means of the thermal Green function. In Section 3 we discuss “clock synchronization” and “clock rate synchronization” in general relativity, and give a condition on “clock rate synchronization” which is different from that given by Landau and Lifshitz. We present a conclusion and discussion in Section 4.

**Zhao Zheng & Ping Chen “**Zeroth Law of Thermodynamics and Transitivity of Simultaneity**,” International Journal of Theoretical Physics, 36(10), 2153-2159 (1997).**