1. wwilson@uco.edu Entropy and the Thermodynamics of a Single Particle W. J. Wilson Department of Engineering and Physics University of Central Oklahoma Edmond, OK 73034 2012 Oklahoma Academy of Sciences Annual Technical Meeting University of Central Oklahoma Edmond, OK November 9, 2012

2. wwilson@uco.edu First Law – Sign Convention Chemistry and Physics sign convention

3. wwilson@uco.edu For a single particle, U = KE+PE = U(x,v) and F = F(x,v) are functions of position and velocity only so if we use the work on system positive sign convention which becomes for a free(non-relativistic) particle,

4. wwilson@uco.edu Now if the change dx and dv occur in time dt So for a single particle system,

5. wwilson@uco.edu So for a single particle system, And for a closed system (no energy allowed to enter or escape) (i.e., an “Adiabatic” Process) We find

6. wwilson@uco.edu So for a single particle system, using the work done on the system is positive sign convention, 1.Yields Newton’s 2 nd Law in the standard form 2.Particle motions governed by Newton’s 2 nd Law correspond to “adiabatic” processes

7. wwilson@uco.edu Generalized Newton’s 2 nd Law For a single particle, or

8. wwilson@uco.edu Now if the change dx and dv occur in time dt So for a single particle, isothermal system

9. wwilson@uco.edu So, Or Generalized 2 nd Law !

10. wwilson@uco.edu The extra “Force-Like” term in is an entropic force or

11. wwilson@uco.edu Entropic Force Example Long Chain Molecules

12. wwilson@uco.edu Expansion of Universe is Accelerating 2011 Physics Nobel Prize Saul Perlmutter (Lawrence Berkeley Lab) Brian Schmidt (Australian National Lab) Adam Reiss (Johns Hopkins)

13. wwilson@uco.edu Dark Energy as Entropic Force? Accelerating expansion

14. wwilson@uco.edu Summary 1 st Law of Thermodynamics (TdS = dU – Fdx ) applied to a single particle leads to a generalized 2 nd Law The entropic force term could give an explanation of the observed accelerating expansion of the universe.

15. wwilson@uco.edu 15 References W. J. Wilson, The Thermodynamics of a Single Particle System, 2012 Oklahoma Academy of Sciences Annual Technical Meeting, Durant, OK, November 11, 2011.Slides available at http://cyberphysics.org/wwilson. E.C.G. Stueckelberg and P. B. Scheurer, Thermocinéque Phénoménologique Galiléenne, (Birkhauser, Stuttgart, 1974) P.E. Williams, On a Possible Formulation of Particle Dynamics in Terms of Thermodynamics Conceptualizations and the Role of Entropy in It (M.S. Thesis, Naval Postgraduate School, Monterey, CA, 1976).