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DY: Fachverband Dynamik und Statistische Physik

DY 11: Focus Session: Thermodynamics and Statistical Physics of Small Systems

DY 11.2: Invited Talk

Tuesday, March 15, 2011, 10:30–11:00, HÜL 186

Microcanonical singularities in finite systems — •Jörn Dunkel¹ and Stefan Hilbert² — ¹Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK — ²Instititut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

The microcanonical equations of state of a finite isolated system can exhibit a substantially more complex structure than their canonical counterparts [1,2]. Prominent examples are singularities and oscillations in the caloric temperature curves, corresponding to regions of negative specific heat, which reflect structural changes in the microscopic properties of the underlying Hamiltonian system as the energy control parameter is varied. After taking a brief look at the virtues and drawbacks of competing microcanonical entropy definitions, we will illustrate the aforementioned phenomena by means of an exactly solvable 1D dissociation model [1]. Although the model is relatively simple, it suggests an interesting general connection between the microscopic temperature oscillations in a finite microcanonical system and macroscopic canonical phase transitions in the corresponding infinite system.

[1] S. Hilbert and J. Dunkel, Phys. Rev. E 74: 011120, 2006

[2] J. Dunkel and S. Hilbert, Physica A 370(2): 390, 2006