Entropic Formulation of Statistical Mechanics

  title={Entropic Formulation of Statistical Mechanics},
  author={Antoni Planes and Eduard Vives},
  journal={Journal of Statistical Physics},
  • A. Planes, E. Vives
  • Published 1 February 2002
  • Mathematics
  • Journal of Statistical Physics
We present an alternative formulation of Equilibrium Statistical Mechanics which follows the method based on the maximum statistical entropy principle in Information Theory combined with the use of Massieu–Planck functions. The different statistical ensembles are obtained by a suitable restriction of the whole set of available microstates. The main advantage is that all of the equations that relate the average values with derivatives of the partition function are formally identical in the… 
Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally
General H-Theorem for Hard Spheres
The maximum entropy formalism is used to investigate the growth of entropy (H-theorem) for an isolated system of hard spheres in an external potential under general boundary geometry. Assuming that
0 30 40 13 v 1 1 0 A pr 2 00 3 Squeezed Statistical Mechanics
We present a formulation of Statistical Mechanics based on the concept of the dimensionless characteristic thermodynamic function, which has the form of a negative Massieu-Planck generalized
Statistical thermodynamics of long-range interacting systems and near-field thermal radiation
[eng] Two main topics are examined in this thesis: classical systems with long-range interactions and thermal radiation in the near-field regime. In the first part, we present a thermodynamic
Thermodynamic extension of density-functional theory. I. Canonical Massieu-Planck function, its Legendre and Massieu-Planck transforms for equilibrium state in terms of density matrix
A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is
Number fluctuation and the fundamental theorem of arithmetic.
  • M. Tran, R. K. Bhaduri
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
This work considers N bosons occupying a discrete set of single-particle quantum states in an isolated trap, and finds that the ground state fluctuation vanishes exactly for all excitations.
Nonequilibrium Free Energy Methods Applied to Magnetic Systems: The Degenerate Ising Model
In this paper, we review the physical concepts of the nonequilibrium techniques for the calculation of free energies applied to magnetic systems using Monte Carlo simulations of different
Physical Chemistry in Depth
1 Mathematics of Thermodynamics.- 2 Foundations of Thermodynamics.- 3 The Laws of Thermodynamics.- 4 Equations of State.- 5 Thermodynamic Processes.- 6 Equilibrium.- 7 The Phase Rule.- 8 Trouton's
Force distribution in a semiflexible loop.
This work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system.
Uncertainty and Certainty Property Estimation of Organizational-Economic System
Uncertainty as a self-condition of open stochastic system is a principium of development of risk representations and their influences on organizational-economic subjects and objects. Undoubtedly,


Information Theory and Statistical Mechanics
Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between
Maximum entropy, fluctuations and priors
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are
A modern course in statistical physics
THERMODYNAMICS. Introduction to Thermodynamics. The Thermodynamics of Phase Transitions. CONCEPTS FROM PROBABILITY THEORY. Elementary Probability Theory and Limit Theorems. Stochastic Dynamics and
Thermodynamic Uncertainty Relations
Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking their
Grand Partition Functions and So‐Called ``Thermodynamic Probability''
The relation due to Boltzmann between entropy and ``thermodynamic probability'' is enunciated in a precise form. This relation is generalized in such a way that each of the other thermodynamic
A mathematical theory of communication
  • C. Shannon
  • Computer Science, Mathematics
    Bell Syst. Tech. J.
  • 1948
In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a
Statistical Mechanics (Pergamon Press, Oxford, 1972)
  • 1st ed. and (Butterworth–Heinemann,
  • 1996
Statistical Mechanics (Elsevier
  • Science, Amsterdam,
  • 1988
Foundations of Statistical Mechanics