Definitions: the primitive concept of logics or The Leśniewski–Tarski legacy

2002 ◽  
Vol 401 ◽  
pp. 1-184 ◽  
Author(s):  
E. G. K. López-Escobar ◽  
Francisco Miraglia
Keyword(s):  
Primitive Concept

STATISTICAL ORIGIN OF SPECIAL AND DOUBLY SPECIAL RELATIVITY

2013 ◽  
Vol 23 ◽  
pp. 373-378
Author(s):  
PETR JIZBA ◽  
FABIO SCARDIGLI
Keyword(s):  
Brownian Motion ◽  
Special Relativity ◽  
Coarse Graining ◽  
Relativistic Motion ◽  
Relativistic Dynamics ◽  
Compton Wavelength ◽  
Primitive Concept ◽  
Short Scale ◽  
Doubly Special Relativity ◽  
First Time

We show how a Brownian motion on a short scale can originate a relativistic motion on scales larger than particle's Compton wavelength. Special relativity appears to be not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Our scheme accommodates easily also the doubly special relativistic dynamics. A previously unsuspected, common statistical origin of the two frameworks is brought to light for the first time.

scholarly journals Second Law and Non-Equilibrium Entropy of Schottky Systems --Doubts and Verification--

2018 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Open Systems ◽  
Embedding Theorem ◽  
Contact Temperature ◽  
Second Law ◽  
Molar Entropy ◽  
Primitive Concept ◽  
Historical Remark ◽  
Clausius Inequality ◽  
Non Equilibrium

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

SUPERSTATISTICS APPROACH TO DOUBLY SPECIAL RELATIVITY

2012 ◽  
Vol 26 (12) ◽  
pp. 1241003 ◽  
Author(s):  
PETR JIZBA ◽  
FABIO SCARDIGLI
Keyword(s):  
Special Relativity ◽  
Spatial Scale ◽  
Wiener Process ◽  
Path Integral ◽  
Coarse Graining ◽  
Relativistic Motion ◽  
Relativistic Dynamics ◽  
Compton Wavelength ◽  
Primitive Concept ◽  
Doubly Special Relativity

Using the concept known as a superstatistics path integral we show that a Wiener process on a short spatial scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Here we place a special emphasis on the modifications that are necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is revealed. Salient issues such as generalized commutation relations and a connection with Feynman chessboard model are also discussed.

scholarly journals Discrete systems in thermal physics and engineering: a glance from non-equilibrium thermodynamics

2021 ◽  
Author(s):  
W. Muschik
Keyword(s):  
Discrete Systems ◽  
Embedding Theorem ◽  
Contact Temperature ◽  
State Function ◽  
Thermal Physics ◽  
Temperature Changes ◽  
Primitive Concept ◽  
Equilibrium Processes ◽  
Cyclic Processes ◽  
Non Equilibrium

AbstractNon-equilibrium processes in Schottky systems generate by projection onto the equilibrium subspace reversible accompanying processes for which the non-equilibrium variables are functions of the equilibrium ones. The embedding theorem which guarantees the compatibility of the accompanying processes with the non-equilibrium entropy is proved. The non-equilibrium entropy is defined as a state function on the non-equilibrium state space containing the contact temperature as a non-equilibrium variable. If the entropy production does not depend on the internal energy, the contact temperature changes into the thermostatic temperature also in non-equilibrium, a fact which allows to use temperature as a primitive concept in non-equilibrium. The dissipation inequality is revisited, and an efficiency of generalized cyclic processes beyond the Carnot process is achieved.

Sign in / Sign up

Export Citation Format

Share Document