A Geometric, Dynamical Approach to Thermodynamics

Details A Geometric, Dynamical Approach to Thermodynamics A Geometric, Dynamical Approach to Thermodynamics

1997-03-21

arxiv.org/abs/chao-dyn/9703013v2

Nonlinear Sciences

Chaotic Dynamics

7 pages, LaTeX, uses RevTex. New sections and examples using fluctuations in the kinetic energy added

Scientific paper

10.1088/0305-4470/31/38/011

We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself micro-canonically observable. In particular, temperature, specific heat and higher order derivatives of the entropy can be observed dynamically. We give perturbative, asymptotic formulas by which the canonical ensemble itself can be reconstructed from micro-canonical measurements only. In a purely micro-canonical approach we rederive formulas by Lebowitz et al \cite{LPV}, relating e.g. specific heat to fluctuations in the kinetic energy. We show that under natural assumptions on the fluctuations in the kinetic energy the micro-canonical temperature is asymptotically equivalent to the standard canonical definition using the kinetic energy.

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