Vol. 3, 10a. “On Boltzmann’s Principle and Some of Its
[Zurich, 2 November 1910]
Thermodynamics is known to be based on two principles, the energy principle
(also called the 1st law) and the principle of the irreversibility of natural events
(also called the 2nd law). This latter principle by states, The substance of this lat-
ter principle can be expressed in the Planckian sense thus, according to Planck
is founded on the presumption of an unbroken entirely
causal relation for all occurrences. Let us assume that Galileo had found from his
pendulum experiments that the period of one oscillation of this pendulum changed
in a very irregular way. Let us assume furthermore that this change could not be
connected with any change in other observable relations. Then it would have been
impossible for Galileo to gather his observations under a law. If all phenomena
accessible to us had as irregular a character as we have just pictured in this fictitious
case, people would certainly never have resorted to scientific endeavors.
Which characteristic must phenomena have in order for science to be possible?
To this, one might first want to reply somewhat as follows: If we put a system into
a particular state, then provided this system is separated from other systems—such
as by a large spatial distance—then over time the course of the states of this system
is completely determined; i.e., if we put two arbitrarily many equally composed
isolated systems into exactly the same state and leave these systems alone, then the
evolution of the phenomena in time is exactly the same for all these systems.
Now, how about the unbroken entirely causal connection between events
according to our knowledge today? This question has to be specified more pre-
cisely before it can be solved. Let us do this right away by means of an example.
Take a cube of copper of a given size. Within this cube we imagine we establish
by external influences a very specific temperature distribution and then, after hav-
ing enveloped it in a thermally insulating shell, we leave it be. We know that in the
course of time a temperature equilibrium will then set in by the process of thermal
conduction. The temperature gradient at all points of the cube will thereby prove to
be “uniquely determined” by the initial state; by the expression “uniquely deter-
mined” we mean that we are always going to perceive the same temperature gradi-
ents, no matter how often we may repeat the experiment, that is, no matter how
often we may set the starting temperature distribution and then leave the cube be.
Does this unique determinability of the process, this entirely causal connection of
events really exist? In order to address a pertinent objection but of no interest to us