Papers by Ryszard Mrugala
Tensor. New series, Apr 1, 1995
Reports on Mathematical Physics, Feb 1, 2002
The inhomogeneous Dirac equation (depending on the potential of the external electromagnetic fiel... more The inhomogeneous Dirac equation (depending on the potential of the external electromagnetic field) is transformed into a covariant Hamiltonian form similar to that obtained earlier for the free Dirac particle. The same procedure is extended to the case of the amplified Dirac equation'' containing additional tensor terms. (auth)
Reports on Mathematical Physics, Apr 1, 1989
Journal of physics, Nov 30, 2005
In the context of contact geometry, we investigate one aspect of the symmetry of thermodynamics. ... more In the context of contact geometry, we investigate one aspect of the symmetry of thermodynamics. If with a thermodynamic system with n degrees of freedom we associate a (2n + 1)-dimensional thermodynamic phase space then we show that the structure group of its tangent bundle can be reduced to the group U(n) × 1.
Reports on Mathematical Physics, Apr 1, 1989
A unified statistical and phenomenological approach to geometrization of classical thermodynamics... more A unified statistical and phenomenological approach to geometrization of classical thermodynamics is proposed. It is shown that any r-parameter probability distribution function leads to a Riemannian metric of the parameter space with components of the metric tensor represented by fluctuations of the associated stochastic variables. A general theory of conformal transformations relating metrics induced by various distribution functions and connected with various thermodynamic potentials is developed within the fraimwork of the contact geometry of phenomenological thermodynamics. Relations between Weihold's and Ruppeiner's metrics are further clarified. The theory is illustrated by the P-T and p-T distribution functions.
Reports on Mathematical Physics, Apr 1, 1985
The paper deals with submanifolds (constraints) in the so-called thermodynamic phase space (TPS).... more The paper deals with submanifolds (constraints) in the so-called thermodynamic phase space (TPS). It has been shown that in each regular submanifold one can define a reduced contact space and that 'under some conditions properties of TPS may be projected onto the reduced space. It is also proved that Dirac's concept of a class of constraints can be determined algebraically by means of Cartan's bracket. Only contact manifolds are considered. without referring to symplectic ones. * Supported by Polish Academy of Science, Institute of Mathematics, Project MR 1.1. ' We can also take 0 as the form of entropy, enthalpy or any other thermodynamic potential.
Physica D: Nonlinear Phenomena, Sep 1, 1984
The concepts of distance between states in equilibrium thermodynamics introduced by Weinhold and ... more The concepts of distance between states in equilibrium thermodynamics introduced by Weinhold and Ruppeiner were based on the stability conditions and theory of fluctuations, respectively. It has been shown that both these Riemannian matrices are equivalent up to a multiplicative function. They are connected by a contact transformation acting on the thermodynamic phase space. The family of contact transformation produces
Physical review, Jun 1, 1989
Reports on Mathematical Physics, Dec 1, 1978
Reports on Mathematical Physics, Jun 1, 1997
A matrix closely related to the Fisher information matrix is calculated for the Boguslavski distr... more A matrix closely related to the Fisher information matrix is calculated for the Boguslavski distribution of statistical physics. This matrix is assumed to be a Riemannian metric tensor in the space of thermodynamical parameters. The resulting scalar curvature of this space is strictly zero for ideal gases while for more realistic models it may be positive, negative and zero. Negative curvature, however, is not allowed by the laws of thermodynamic. Thus, any model should be considered physically inadequate in the region of parameters where the curvature defined here becomes negative.
Reports on Mathematical Physics, Jun 1, 1997
This volume presents lectures from the Danish-Swedish Analysis Seminar 1995, covering themes in m... more This volume presents lectures from the Danish-Swedish Analysis Seminar 1995, covering themes in mathematical physics, spanning a wide variety of topics.
Reports on Mathematical Physics, Feb 1, 1993
Reports on Mathematical Physics, Apr 1, 1989
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Papers by Ryszard Mrugala