Abstract (17.0: Equilibrium statistical mechanics and Ergodic Hypothesis)
In this chapter, we study and answer the following fundamental
problems concerning
classical
equilibrium
statistical mechanics:
$(A):$
Is the principle of equal a priori probabilities
indispensable for
equilibrium statistical mechanics?
$(B):$
Is
the ergodic hypothesis
related to
equilibrium statistical mechanics?
Note that
there are several opinions for the formulation
of
equilibrium
statistical mechanics.
In this sense,
the above problems are not yet answered.
Thus we
propose
the measurement theoretical foundation
of
equilibrium
statistical mechanics, and clarify
the confusion between
two aspects
(i.e.,
probabilistic and kinetic aspects
in
equilibrium
statistical mechanics),
that is,
we discuss
$(C):$
Why and where does the concept of "probability" appear in
equilibrium statistical mechanics?
$\bullet$
$
\begin{cases}
\mbox{the kinetic aspect (i.e., causality)}
&
\cdots
\mbox{ in Section 17.1}
\\
\mbox{the probabilistic aspect (i.e., measurement) }
&
\cdots
\mbox{ in Section 17.2}
\end{cases}
$
And we answer the above (A) and (B),
that is,
we conclude that
and further, we can understand the problem (C).
This chapter is extracted from the following:
$(\sharp )$
(A) is "No",
but,
(B) is "Yes"
$\bullet$
S.Ishikawa, Equilibrium Statistical Mechanics
in the Quantum Mechanical World View
World Journal of Mechanics,
Vol. 2, No. 2, 2012, pp. 125-130
17.0:Equilibrium statistical mechanics and Ergodic Hypothesis
This web-site is the html version of "Linguistic Copehagen interpretation of quantum mechanics; Quantum language [Ver. 4]" (by Shiro Ishikawa; [home page] )
PDF download : KSTS/RR-18/002 (Research Report in Dept. Math, Keio Univ. 2018, 464 pages)