Sunday, May 19, 2013

1305.3724 (Yoshimasa Kurihara et al.)

Thermodynamics for Trajectories of a Mass Point    [PDF]

Yoshimasa Kurihara, Nhi My Uyen Quach
New formalism of classical non-relativistic mechanics of a mass point is proposed based on an information theoretical point of view. Particle trajectories of a general dynamical system defined in (1+n)-dimensional smooth manifold are treated as dynamical variables using a geometrical method. Statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamical variables are introduced through a partition function based on a canonical ensemble of trajectories. In this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. %This point of view suggests us to interpret that quantum mechanics belongs to non-equilibrium states of classical trajectories. A relation among our formalism, path-integral and stochastic quantizations is also discussed. A relation between classical and quantum mechanics are discussed from this statistical mechanical point of view.
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