Microcanonical phase transitions in small systems

Michele Campisi

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Microcanonical phase transitions in small systems

Michele Campisi

Statistical Mechanics · Submitted 7 Sep 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For systems with broken ergodicity, the volume entropy has discontinuous jumps at values of energy that correspond to separatrix trajectories.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,618 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

When studying the thermodynamic properties of mesoscopic systems the most appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of the volume of phase space enclosed by the hypersurface of constant energy. For systems with broken ergodicity, the volume entropy has discontinuous jumps at values of energy that correspond to separatrix trajectories. Simultaneously there is a convex intruder in the entropy function and a region of negative specific heat below such critical energies. We illustrate this with a simple model composed of a chain of 3 particles which interact via a Lennard-Jones potential.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	When studying the thermodynamic properties of mesoscopic systems the most appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of the volume of phase space enclosed by the hypersurface of constant energy.	background 0.99	0.10	0.13	asserted 1.00
s1	For systems with broken ergodicity, the volume entropy has discontinuous jumps at values of energy that correspond to separatrix trajectories.	result 0.68	0.20	0.22	asserted 1.00
s2	Simultaneously there is a convex intruder in the entropy function and a region of negative specific heat below such critical energies.	result 0.90	0.32	0.30	asserted 1.00
s3	We illustrate this with a simple model composed of a chain of 3 particles which interact via a Lennard-Jones potential.	method 0.92	0.90	0.03	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.83 · evidence from simulation or computation 0.74.

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arXiv listing abstract v1

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full text
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T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

When studying the thermodynamic properties of mesoscopic systems the most appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of the volume of phase space enclosed by the hypersurface of constant energy. For systems with broken ergodicity, the volume entropy has discontinuous jumps at values of energy that correspond to separatrix trajectories. Simultaneously there is a convex intruder in the entropy function and a region of negative specific heat below such critical energies. We illustrate this with a simple model composed of a chain of 3 particles which interact via a Lennard-Jones potential.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as support 2 papers

Very recently it has been also proved that non-adiabatic transformations occurring in isolated systems which are initially in a state of thermal equilibrium always result in an increase of the expectation value of the volume entropy [ref] .

Mechanical Proof of the Second Law of Thermodynamics Based on Volume Entropy · Why volume entropy · 0.96
Very recently it has been also proved that non-adiabatic transformations occurring in isolated systems which are initially in a state of thermal equilibrium always result in an increase of the expectation value of the volume entropy [ref] .

Statistical mechanical derivation of the second law of thermodynamics · Why volume entropy · 0.96

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