About the role of chaos and coarse graining in statistical mechanics

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.

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Statistical mechanics of coarse graining: Estimating dynamical speedups from excess entropies

The Journal of Chemical Physics ◽

10.1063/1.3697383 ◽

2012 ◽

Vol 136 (12) ◽

pp. 124503 ◽

Cited By ~ 12

Author(s):

J. A. Armstrong ◽

C. Chakravarty ◽

P. Ballone

Keyword(s):

Statistical Mechanics ◽

Coarse Graining

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THE HATSOPOULOS–GYFTOPOULOS RESOLUTION OF THE SCHRÖDINGER–PARK PARADOX ABOUT THE CONCEPT OF "STATE" IN QUANTUM STATISTICAL MECHANICS

Modern Physics Letters A ◽

10.1142/s0217732306021840 ◽

2006 ◽

Vol 21 (37) ◽

pp. 2799-2811 ◽

Cited By ~ 5

Author(s):

GIAN PAOLO BERETTA

Keyword(s):

Information Theory ◽

Quantum Theory ◽

Statistical Mechanics ◽

Quantum Statistical Mechanics ◽

Quantum Information Theory ◽

Individual State ◽

Fundamental Difficulty ◽

Quantum Statistical ◽

Theory Interpretation

A seldom recognized fundamental difficulty undermines the concept of individual "state" in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by Schrödinger in 1936 and perused by Park, Am. J. Phys.36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resolution proposed in 1976 by Hatsopoulos and Gyftopoulos, Found. Phys.6, 15; 127; 439; 561 (1976).

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