Stochastic Thermodynamics Across Scales: Emergent Inter-attractoral Discrete Markov Jump Process and Its Underlying Continuous Diffusion

The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete, inter-attractoral Markov jump process, is investigated. We analyze how the system's thermodynamic state functions, e.g. free energy $F$, entropy $S$, entropy production $e_p$, and free energy dissipation $\dot{F}$, etc., are related when the continuous system is describe with a coarse-grained discrete variable. We show that the thermodynamics derived from the underlying detailed continuous dynamics is exact in the Helmholtz free-energy representation. That is, the system thermodynamic structure is the same as if one only takes a middle-road and starts with the "natural" discrete description, with the corresponding transition rates empirically determined. By "natural", we mean in the thermodynamic limit of large systems in which there is an inherent separation of time scales between inter- and intra-attractoral dynamics. This result generalizes a fundamental idea from chemistry and the theory of Kramers by including thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described by the Law of Mass Action with rate constants, and a stochastic thermodynamics.Comment: 21 pages, 1 figur

Ethyl 8-(4-nitro­phen­yl)imidazo[1,2-a]pyridine-7-carboxyl­ate

In the title compound, C16H13N3O4, the imidazo[1,2-a]pyridine and benzene rings make a dihedral angle of 56.21 (2)°. The crystal packing is stabilized by weak π–π stacking inter­actions [centroid–centroid distances = 3.787 (2) Å] and C—H⋯O inter­molecular hydrogen-bonding inter­actions

Statistical significance and publication reporting bias in abstracts of reproductive medicine studies

Funding Information: We thank Dr David Chavalarias from Complex Systems Institute of Paris Ile-de-France for sharing scripts in extracting P-values. B.W.M. is supported by an National Health and Medical Research Council (NHMRC) Investigator grant (GNT1176437); B.W.M. reports consultancy, research grants, and travel support from Merck. W.L. is supported by an NHMRC Investigator Grant (GNT2016729). Q.F. reports receiving a PhD scholarship from Merck. The other author has no conflict of interest to declare. Funding Information: B.W.M. is supported by an National Health and Medical Research Council (NHMRC) Investigator grant (GNT1176437); B.W.M. reports consultancy, research grants, and travel support from Merck. W.L. is supported by an NHMRC Investigator Grant (GNT2016729). Q.F. reports receiving a PhD scholarship from Merck. The other author has no conflict of interest to declare. Publisher Copyright: © 2024 Oxford University Press. All rights reserved.Peer reviewe

3,5-Bis[1-acetyl-5-(4-chloro­phen­yl)-4,5-dihydro-1H-pyrazol-3-yl]-2,6-dimethyl­pyridine

The title compound, C29H27Cl2N5O2, contains a central pyridine ring and two functionalized pyrazoline rings. The pyridine ring and the two attached pyrazoline rings are nearly coplanar, whereas the terminal chloro­phenyl rings are nearly perpendicular to the attached pyrazoline rings [dihedral angles = 86.78 (1) and 77.70 (1)°]. Mol­ecules are linked by weak inter­molecular C—H⋯O hydrogen bonding

Cdc42 and Tinman march to the same beat

Study describes a conserved genetic network that regulates heart function in flies and mammals

Ethyl 1-(4-chloro­benz­yl)-3-phenyl-1H-pyrazole-5-carboxyl­ate

In the title compound, C19H17ClN2O2, the pyrazole ring makes dihedral angles of 6.97 (5) and 79.25 (1)°, respectively, with the phenyl and chlorophenyl rings, respectively. In the crystal, C—H⋯O hydrogen bonds are observed

Applying a simplified economic evaluation approach to evaluate infertility treatments in clinical practice

Peer reviewe