Physics
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufmsm21b1893n&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #SM21B-1893
Physics
[2744] Magnetospheric Physics / Magnetotail, [2772] Magnetospheric Physics / Plasma Waves And Instabilities, [2799] Magnetospheric Physics / General Or Miscellaneous
Scientific paper
It is known that space plasmas often have non-equilibrium distribution functions because their binary collision frequencies are extremely low. Given a non-equilibrium distribution f(x,v), it is possible to calculate information theoretic entropy by integrating f log f. However, it is known (though not well understood) that the information theoretic entropy is not directly related to thermodynamical entropy; thermodynamical entropy is defined only when the system is in equilibrium. For instance, we do not know how to relate information theoretic entropy to thermodynamical quantities such as free energy when the system is not in equilibrium. This is a controversial point in statistical physics and some experts consider the information theoretic entropy has nothing to do with thermodynamical entropy in general and the equilibrium state is the only exception. However, we plasma physicists intuitively believe that non-equilibrium distribution has some kind of "free energy"; we expect unstable non-equilibrium distribution causes instability because of the "free energy". On the other hand, we know the information theoretic entropy calculated from Vlasov equation does not change since there is no collisions. To obtain entropy change, we must introduce coarse-grained distribution function. It can be shown that the entropy calculated from coarse-grained distribution function may change in time, however, there is no proof it is a monotonically increasing function so far. Moreover, the value of the entropy from coarse-grained function depends on the scale of coarse-graining and thus, it cannot be regarded as a physical quantity. The purpose of the present paper is to define "free energy" based on the information theoretic entropy. Two assumptions are postulated to this end: (1) information theoretic entropy does not decrease in a isolated system; (2) information theoretic entropy corresponds to thermodynamical entropy when the distribution function is Maxwellian. In the presentation, discussions will be given on the plausibility of these assumptions as well as the tactics for actual calculation of "free energy".
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