# Study Notes **URL:** \ **Category:** General\ **Created:** [October 1, 2021, 9:55pm UTC](http://forum.0xdbfb7.com/t/study-notes/85 "2021-10-01T21:55:15Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![0xDBFB7](http://forum.0xdbfb7.com/user_avatar/forum.0xdbfb7.com/0xdbfb7/32/7_2.png) [@0xDBFB7](http://forum.0xdbfb7.com/u/0xDBFB7)\ **Post date:** [October 1, 2021, 9:55pm UTC](http://forum.0xdbfb7.com/t/study-notes/85/1 "2021-10-01T21:55:15Z")
# Module 1 The Lagrangian L = T-V, where T is the kinetic energy and V the potential energy. Can be re-written in terms of a variable q, which might as well be x. Action is denoted S. The hamiltonian is the total energy of the system; {\cal H}=T+V U is internal energy; defined as the sum of all kinetic and potential energies present in the system. Q is heat W is work dU = \delta Q + \delta W; this is called the “total differential of” U Both Q (heat) and W (work) are path variables. A subscript variable like \left(\frac{dS}{dT}\right)\_{V} means “held constant”. A “harmonic” potential has V \approx a x^2; that is, F \approx bx. ## Conjugate variable The thermodynamic identity is dU = T dS - p dV + \sum \mu \ dN [https://en.wikipedia.org/wiki/Conjugate\_variables\_(thermodynamics)](https://en.wikipedia.org/wiki/Conjugate_variables_(thermodynamics)) [https://www.aapt.org/docdirectory/meetingpresentations/sm14/mungan-poster.pdf](https://www.aapt.org/docdirectory/meetingpresentations/sm14/mungan-poster.pdf) ---
**Author:** ![0xDBFB7](http://forum.0xdbfb7.com/user_avatar/forum.0xdbfb7.com/0xdbfb7/32/7_2.png) [@0xDBFB7](http://forum.0xdbfb7.com/u/0xDBFB7)\ **Post date:** [October 24, 2021, 2:46pm UTC](http://forum.0xdbfb7.com/t/study-notes/85/2 "2021-10-24T14:46:11Z")
Extensive: internal energy depends linearly on the size of the system: > Likewise for the [density](https://en.wikipedia.org/wiki/Density) of a homogeneous system; if the system is divided in half, the extensive properties, such as the mass and the volume, are each divided in half, and the intensive property, the density, remains the same in each subsystem. [http://snst-hu.lzu.edu.cn/zhangyi/ndata/Conjugate\_variables\_(thermodynamics).html](http://snst-hu.lzu.edu.cn/zhangyi/ndata/Conjugate_variables_%28thermodynamics%29.html) ---
**Author:** ![0xDBFB7](http://forum.0xdbfb7.com/user_avatar/forum.0xdbfb7.com/0xdbfb7/32/7_2.png) [@0xDBFB7](http://forum.0xdbfb7.com/u/0xDBFB7)\ **Post date:** [October 24, 2021, 3:54pm UTC](http://forum.0xdbfb7.com/t/study-notes/85/3 "2021-10-24T15:54:47Z")
# Quantum mechanics Probability of finding a particle at a point is the squared amplitude. \Psi is a wave-packet; P = |\Psi(q,t)|^2. A system satisifying the “markovian property” is memoryless: the future state depends only upon the present state, not past states. ---
**Author:** ![0xDBFB7](http://forum.0xdbfb7.com/user_avatar/forum.0xdbfb7.com/0xdbfb7/32/7_2.png) [@0xDBFB7](http://forum.0xdbfb7.com/u/0xDBFB7)\ **Post date:** [October 26, 2021, 5:52pm UTC](http://forum.0xdbfb7.com/t/study-notes/85/4 "2021-10-26T17:52:14Z")
## Conjugate variables The thermodynamic identity is [http://snst-hu.lzu.edu.cn/zhangyi/ndata/Conjugate\_variables\_(thermodynamics).html](http://snst-hu.lzu.edu.cn/zhangyi/ndata/Conjugate_variables_%28thermodynamics%29.html) ---
**Author:** ![0xDBFB7](http://forum.0xdbfb7.com/user_avatar/forum.0xdbfb7.com/0xdbfb7/32/7_2.png) [@0xDBFB7](http://forum.0xdbfb7.com/u/0xDBFB7)\ **Post date:** [October 26, 2021, 5:57pm UTC](http://forum.0xdbfb7.com/t/study-notes/85/5 "2021-10-26T17:57:47Z")
> **[Onsager reciprocal relations](https://en.wikipedia.org/wiki/Onsager_reciprocal_relations)** > > In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists. > "Reciprocal relations" occur between different pairs of forces and flows in a variety of physical systems. For example, consider fluid systems described in terms of temperature, matter density, and pressure. In this class of systems, it is known that temperature differences lead to heat flo... explains the seebeck effect etc ---
**Author:** ![0xDBFB7](http://forum.0xdbfb7.com/user_avatar/forum.0xdbfb7.com/0xdbfb7/32/7_2.png) [@0xDBFB7](http://forum.0xdbfb7.com/u/0xDBFB7)\ **Post date:** [October 30, 2021, 5:15pm UTC](http://forum.0xdbfb7.com/t/study-notes/85/6 "2021-10-30T17:15:11Z")
# Module 3.1 The n-th “moment” of a probability distribution is The poisson distribution has a mean value equal to its first moment. > “If the function is a [probability distribution](https://en.wikipedia.org/wiki/Probability_distribution), then the first moment is the [expected value](https://en.wikipedia.org/wiki/Expected_value), the second [central moment](https://en.wikipedia.org/wiki/Central_moment) is the [variance](https://en.wikipedia.org/wiki/Variance), the third [standardized moment](https://en.wikipedia.org/wiki/Standardized_moment) is the [skewness](https://en.wikipedia.org/wiki/Skewness), and the fourth standardized moment is the [kurtosis](https://en.wikipedia.org/wiki/Kurtosis).” > > - [https://en.wikipedia.org/wiki/Moment\_(mathematics)](https://en.wikipedia.org/wiki/Moment_(mathematics))