There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

By its very nature, the second law of thermodynamics is probabilistic, in that its formulation requires a probabilistic description of the state of a system. This raises questions about the objectivity of the second law: does it depend, for example, on what we know about the system? For over a century, much effort has been devoted to incorporating information into thermodynamics and assessing the entropic and energetic costs of manipulating information. More recently, this historically theoretical pursuit has become relevant in practical situations where information is manipulated at small scales, such as in molecular and cell biology, artificial nano-devices or quantum computation. Here we give an introduction to a novel theoretical framework for the thermodynamics of information based on stochastic thermodynamics and fluctuation theorems, review some recent experimental results, and present an overview of the state of the art in the field. The task of integrating information into the framework of thermodynamics dates back to Maxwell and his infamous demon. Recent advances have made these ideas rigorous—and brought them into the laboratory.

/pdf/thermodynamics-of-information-tfsklm0odf.pdf

Thermodynamics of information

Feedback mechanisms such as the ‘demon’ in Maxwell’s well-known thought experiment can, in principle, enable the transformation of information into energy, without violating the second law of thermodynamics. Such information-to-energy conversion by feedback control has now been demonstrated experimentally.

/pdf/experimental-demonstration-of-information-to-energy-cfx598nnhq.pdf

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

The Jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control. The new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement and the efficacy of the feedback control. Our results lead to a generalized fluctuation-dissipation theorem that reflects the readout information, and they can be experimentally tested using small thermodynamic systems. We illustrate our general results by introducing an "information ratchet", which can transport a Brownian particle in one direction and extract positive work from the particle.

/pdf/generalized-jarzynski-equality-under-nonequilibrium-feedback-43t707nf3j.pdf

Generalized Jarzynski equality under nonequilibrium feedback control.

The fundamental lower bounds on the thermodynamic energy cost of measurement and information erasure are determined. The lower bound on the erasure validates Landauer's principle for a symmetric memory; for other cases, the bound indicates the breakdown of the principle. Our results constitute the second law of "information thermodynamics," in which information content and thermodynamic variables are treated on an equal footing.

/pdf/minimal-energy-cost-for-thermodynamic-information-processing-j8djtwlaeq.pdf

Minimal energy cost for thermodynamic information processing: measurement and information erasure.

A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat-baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller.

Takahiro Sagawa

Papers

Thermodynamics of information

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

Generalized Jarzynski equality under nonequilibrium feedback control.

Minimal energy cost for thermodynamic information processing: measurement and information erasure.

Second law of thermodynamics with discrete quantum feedback control.