On the way to the mathematical foundations of statistical mechanics

1993 ◽  
pp. 1-37
Author(s):  
R. L. Dobrushin
Keyword(s):  
Statistical Mechanics ◽  
Foundations Of Statistical Mechanics ◽  
Mathematical Foundations ◽  
The Way

scholarly journals Mathematical foundations of statistical mechanics.

1949 ◽  
Vol 26 (12) ◽  
pp. 685
Author(s):  
Pierre Van Rysselberghe
Keyword(s):  
Statistical Mechanics ◽  
Foundations Of Statistical Mechanics ◽  
Mathematical Foundations

Mathematical Foundations of Nonextensive Statistical Mechanics

10.1142/12499 ◽  
2022 ◽  
Author(s):  
Sabir Umarov ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Nonextensive Statistical Mechanics ◽  
Mathematical Foundations

scholarly journals An Introduction to the Non-Equilibrium Steady States of Maximum Entropy Spike Trains

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 884 ◽  
Author(s):  
Rodrigo Cofré ◽  
Leonardo Videla ◽  
Fernando Rosas
Keyword(s):  
Statistical Mechanics ◽  
Maximum Entropy ◽  
Spike Trains ◽  
Biological Processes ◽  
Comprehensive Overview ◽  
Equilibrium Statistical Mechanics ◽  
Temporal Asymmetry ◽  
Key Concepts ◽  
Mathematical Foundations ◽  
Non Equilibrium

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the literature of non-equilibrium statistical mechanics. This tutorial provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics.

Foundations of Statistical Mechanics

1988 ◽  
Author(s):  
Walter T. Grandy
Keyword(s):  
Statistical Mechanics ◽  
Foundations Of Statistical Mechanics

Time in Thermodynamics

2011 ◽  
Author(s):  
Jill North
Keyword(s):  
Statistical Mechanics ◽  
Boundary Conditions ◽  
Equilibrium States ◽  
Temporal Asymmetry ◽  
Heat Flows ◽  
Foundations Of Statistical Mechanics ◽  
Open Questions ◽  
Closed Systems ◽  
The Many

It is often claimed, or hoped, that some temporal asymmetries are explained by the thermodynamic asymmetry in time. Thermodynamics, the macroscopic physics of pressure, temperature, volume, and so on, describes many temporally asymmetric processes. Heat flows spontaneously from hot objects to cold objects (in closed systems), never the reverse. More generally, systems spontaneously move from non-equilibrium states to equilibrium states, never the reverse. Delving into the foundations of statistical mechanics, this chapter reviews the many open questions in that field as they relate to temporal asymmetry. Taking a stand on many of them, it tackles questions about the nature of probabilities, the role of boundary conditions, and even the nature and scope of statistical mechanics.

scholarly journals Foundations of statistical mechanics from symmetries of entanglement

2016 ◽  
Vol 18 (6) ◽  
pp. 063013 ◽  
Author(s):  
Sebastian Deffner ◽  
Wojciech H Zurek
Keyword(s):  
Statistical Mechanics ◽  
Foundations Of Statistical Mechanics
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