V O L . 3 , D O C . 1 0 a B O L T Z M A N N ’ S P R I N C I P L E 5 one. Why do we not observe this? Doesn’t this consideration show that the kinetic theory of heat has to be abandoned? This question was answered by Boltzmann, specifically, in [the] following way: Observe some closed physical system having a particular given amount of energy. We signify by all observable states that this system can assume at the given energy value. In the example of the copper cube, each would thus mean a particular temperature distribution, where in total l distinguishable temperature distributions are possible. But now it is assumed that these states Z be of entirely different probabilities, such that from among all the states differing very little from a given state , one be far more probable than all the others, at least provided that differ substantially from the so-c[alled] state of thermodynamic equilib- rium. Then, if brought into the state and then left to itself, the system is far more likely to change into the state than into any other states neighboring state . The probability that this would occur can come as close to unity (i.e., certainty) as you like, although it is excluded in principle that this transition be entirely cer- tain.T[his] m[eans]: If we bring the system very frequently into the state , then in the great majority of cases, but by no means always, state will follow state a transition into every other neighboring state to state will also occasionally occur, even if only extremely rarely. What has been said about the transition from state into neighboring state is again valid for the change a system experi- ences from state in the following little segment of time. Thus one arrives at a conception of (apparently) irreversible processes. This sketch of the Boltzmann conception is incomplete. Still needing to be answered are the questions: “How should the probability of individual states be understood?” and “Why is a transition from one state to the most probable neighboring state more probable than a transition to other neighboring states?” For the first of these questions we note the following: According to the molec- ular th kinetic theory of heat, there cannot be a thermal equilibrium in the strict sense. The state we call a thermal equilibrium is one that a system left to itself for enormously long most frequently has. However, it is a consequence of the kinetic theory that over long periods of time the system will take on all possible states in particular, the further a state is away from thermodynamic equilibrium, the more rarely does the system assume it. The copper cube left infinitely long to itself inces- santly changes its temperature distribution, whereby it extremely seldom assumes temperature distributions differing considerably from the temperature distribution of thermal equilibrium. If we imagine a system under observation for an immensely long time T, there will be for most states an abnormally small portion of this Z1, Z2…Zl Zν Za Zb) ( Za Za Zb Za [p. 5] Za Zb Za Za Za Zb Zb Z1 Z2 …, Za Zb Zν τ