Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Foundations of Physics

From phenomenological thermodynamics to the canonical ensemble

H. A. Buchdahl

Published Dec 1, 1979• 3 citations
Publisher
DOI
10.1007/bf00708695

Related papers

Thermodynamics of Finite Bose Systems: An Exact Canonical-Ensemble Treatment with Different Traps

Jianhui Wang, Yongli Ma, Jizhou He

Journal of Low Temperature Physics•Oct 5, 2010•11 citations

Microscopic expression of the second law of thermodynamics

Takaaki Monnai

The microscopic derivation of the second law for macroscopic system is given under the phenomenological assumption that both the initial and final states are described by mutually different canonical ensembles. In particular, it is also shown that the entropy difference between the initial and final states is composed of two positive components. One of the components is expressed as the relative entropy between the initial and final states, while the other is positive due to a dynamical stability called passivity of the canonical ensemble.

arXiv:1005.3464•May 19, 2010•0 citations

Statistical Ensemble and Quantization of Thermodynamics

Виктор Павлович Маслов

Mathematical Notes•Mar 1, 2002•4 citations

Thermodynamics in the Quantum Regime

Felix C. Binder, Luis Alfonso Correa, Christian Gogolin +2 more

Fundamental theories of physics•Jan 1, 2018•527 citations

From phenomenological thermodynamics to the canonical ensemble. II

H. A. Buchdahl

For pt.I see Found. Phys., vol.9, no.11-12, p819-29 (1979). A general assumption made in a previous paper is modified by the elimination of the metrical entropy in favour of empirical entropy. Without reference to absolute temperature or metrical entropy, one then arrives at a generic form of the canonical probability in phase in which temperature does not occur. It is argued that this is as it should be if one looks upon the canonical ensemble as merely being the representative of a system in thermal equilibrium with its surroundings. One motivation for this work is to take a view of 'statistical mechanics' which does away with probabilistic notions altogether.

Journal of Physics A Mathematical and General•Jan 11, 1983•0 citations

Finite-size behaviour of the microcanonical specific heat

H Behringer, M Pleimling, A Hüller

For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system. A phenomenological theory is developed which permits us to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents.

arXiv:cond-mat/0411153•Journal of Physics A Mathematical and General•Jan 20, 2005•24 citations
The microscopic derivation of the second law for macroscopic system is given under the phenomenological assumption that both the initial and final states are described by mutually different canonical ensembles. In particular, it is also shown that the entropy difference between the initial and final states is composed of two positive components. One of the components is expressed as the relative entropy between the initial and final states, while the other is positive due to a dynamical stability called passivity of the canonical ensemble.
For pt.I see Found. Phys., vol.9, no.11-12, p819-29 (1979). A general assumption made in a previous paper is modified by the elimination of the metrical entropy in favour of empirical entropy. Without reference to absolute temperature or metrical entropy, one then arrives at a generic form of the canonical probability in phase in which temperature does not occur. It is argued that this is as it should be if one looks upon the canonical ensemble as merely being the representative of a system in thermal equilibrium with its surroundings. One motivation for this work is to take a view of 'statistical mechanics' which does away with probabilistic notions altogether.
For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system. A phenomenological theory is developed which permits us to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents.