# 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:

- 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}

}