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Title: Microcanonical Thermostatistics, the basis for a New Thermodynamics, 'heat can flow from cold to hot', and nuclear multifragmentation. The correct treatment of Phase Separation after 150 years of statistical mechanics

Abstract

Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic limit are they equivalent to ME for homogeneous systems. Therefore ME is the only ensemble for non-extensive/inhomogeneous systems like nuclei or stars where the limN{yields}{infinity},{rho}=N/V=const does not exist. Conventional canonical thermostatistic is inapplicable for non-extensive systems. This has far reaching fundamental and quite counter-intuitive consequences for thermo-statistics in general: Phase transitions of first order are signaled by convexities of S(E,N,Z, {center_dot}{center_dot}{center_dot}). Here the specific heat is negative. In these cases heat can flow from cold to hot{exclamation_point} The original task of thermodynamics, the description of boiling water in heat engines is solved. Consequences of this basic peculiarity for nuclear statistics as well for the fundamental understanding of Statistical Mechanics in general are discussed. Experiments on hot nuclei show all these novel phenomena in a rich variety. The close similarity to inhomogeneous astro physical systems will be pointed out.

Authors:
 [1]
  1. Hahn Meitner Institut, 14109 Berlin (Germany)
Publication Date:
OSTI Identifier:
21054887
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 884; Journal Issue: 1; Conference: 6. Latin American symposium on nuclear physics and applications, Iguazu (Argentina), 3-7 Oct 2005; Other Information: DOI: 10.1063/1.2710559; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; HOT NUCLEI; LAPLACE TRANSFORMATION; NUCLEAR FRAGMENTATION; PARTITION FUNCTIONS; SPECIFIC HEAT; STATISTICAL MECHANICS; STATISTICAL MODELS; THERMODYNAMICS

Citation Formats

Gross, D. H. E. Microcanonical Thermostatistics, the basis for a New Thermodynamics, 'heat can flow from cold to hot', and nuclear multifragmentation. The correct treatment of Phase Separation after 150 years of statistical mechanics. United States: N. p., 2007. Web. doi:10.1063/1.2710559.
Gross, D. H. E. Microcanonical Thermostatistics, the basis for a New Thermodynamics, 'heat can flow from cold to hot', and nuclear multifragmentation. The correct treatment of Phase Separation after 150 years of statistical mechanics. United States. doi:10.1063/1.2710559.
Gross, D. H. E. Mon . "Microcanonical Thermostatistics, the basis for a New Thermodynamics, 'heat can flow from cold to hot', and nuclear multifragmentation. The correct treatment of Phase Separation after 150 years of statistical mechanics". United States. doi:10.1063/1.2710559.
@article{osti_21054887,
title = {Microcanonical Thermostatistics, the basis for a New Thermodynamics, 'heat can flow from cold to hot', and nuclear multifragmentation. The correct treatment of Phase Separation after 150 years of statistical mechanics},
author = {Gross, D. H. E.},
abstractNote = {Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic limit are they equivalent to ME for homogeneous systems. Therefore ME is the only ensemble for non-extensive/inhomogeneous systems like nuclei or stars where the limN{yields}{infinity},{rho}=N/V=const does not exist. Conventional canonical thermostatistic is inapplicable for non-extensive systems. This has far reaching fundamental and quite counter-intuitive consequences for thermo-statistics in general: Phase transitions of first order are signaled by convexities of S(E,N,Z, {center_dot}{center_dot}{center_dot}). Here the specific heat is negative. In these cases heat can flow from cold to hot{exclamation_point} The original task of thermodynamics, the description of boiling water in heat engines is solved. Consequences of this basic peculiarity for nuclear statistics as well for the fundamental understanding of Statistical Mechanics in general are discussed. Experiments on hot nuclei show all these novel phenomena in a rich variety. The close similarity to inhomogeneous astro physical systems will be pointed out.},
doi = {10.1063/1.2710559},
journal = {AIP Conference Proceedings},
number = 1,
volume = 884,
place = {United States},
year = {Mon Feb 12 00:00:00 EST 2007},
month = {Mon Feb 12 00:00:00 EST 2007}
}
  • No abstract prepared.
  • We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of particles. This enables us to study a phase transition in the model. A first order phase transition can be tracked down. There are significant differences between this phase transition and some other well-known cases. {copyright} {ital 1998} {ital The American Physical Society}
  • The evolution of the symmetry energy coefficient of the binding energy of hot fragments with increasing excitation is explored in multifragmentation processes following heavy-ion collisions below the Fermi energy. In this work, high-resolution mass spectrometric data on isotopic distributions of projectile-like fragments are systematically compared to calculations involving the statistical multifragmentation model (SMM). Within the SMM picture, the present study suggests a gradual decrease of the symmetry energy coefficient of the hot primary fragments from 25 MeV at the compound nucleus regime towards 15 MeV in the multifragmentation regime. The isotopic distributions of the hot primary fragments are found tomore » be very wide and extend towards the neutron drip line. These findings are expected to have important implications in the modeling of the composition and the evolution of hot and dense astrophysical environments, such as those of core-collapse supernova.« less
  • Part I of the study presented the two phases used for the isotope exchange in an idealized form, without considering the solubility of the gas in the liquid or the vapor pressure of the latter. The present article gives two methods for correcting the calculations by including solubility and vapor pressure. (auth)