Thermodynamics: Systems and Properties

Thermodynamics Introduction

• Thermodynamics studies energy, its transformations, and its relation to matter.
• It's based on fundamental laws governing energy behavior.

Key Concepts in Thermodynamics

• A system refers to a defined region in space with boundaries.
• Surroundings include everything outside the defined system.
• The boundary is the surface separating the system from its surroundings.

Types of Thermodynamic Systems

• An isolated system doesn't exchange mass or energy with its surroundings.
• A closed system exchanges energy but not mass with its surrounding environment.
• An open system exchanges both mass and energy with its surrounding environment.

System Properties: Intensive Properties

• Intensive properties do not depend on the substance amount.
• Examples include temperature, pressure, and density.

System Properties: Extensive Properties

• Extensive properties depend directly on the amount of substance.
• Volume, mass, and energy are examples of extensive properties.

Thermodynamic Processes: Isothermal

• An isothermal process happens at a constant temperature (T).
• Here, dT = 0.

Thermodynamic Processes: Isobaric

• An isobaric process occurs at constant pressure (P).
• In this case, dP = 0.

Thermodynamic Processes: Isochoric

• An isochoric process takes place at constant volume (V).
• Thus, dV = 0.

Thermodynamic Processes: Adiabatic

• An adiabatic process involves no heat exchange (Q) with the surroundings.
• Therefore, dQ = 0.

Laws of Thermodynamics: Zeroth Law

• If two systems are in thermal equilibrium with a third, they're in thermal equilibrium with each other.
• It establishes the concept of temperature.

Laws of Thermodynamics: First Law

• The change in internal energy (ΔU) equals the heat added (Q) minus work done (W).
• Expressed as: ΔU = Q - W.
• Reflects the conservation of energy.

Laws of Thermodynamics: Second Law

• The total entropy of an isolated system can only increase or remain constant in ideal conditions.
• Mathematically, ΔS ≥ 0.
• Entropy measures disorder or system randomness.

Laws of Thermodynamics: Third Law

• A perfect crystal's entropy at absolute zero temperature is zero.
• S = 0 at T = 0 K.

Thermodynamic Potentials: Internal Energy (U)

• Represents the total energy contained within a system.
• It's considered a state function.

Thermodynamic Potentials: Enthalpy (H)

• H = U + PV, where P is pressure and V is volume.
• It's useful for constant pressure processes.

Thermodynamic Potentials: Helmholtz Free Energy (A)

• A = U - TS, where T is temperature and S is entropy.
• Its used for constant temperature and volume processes.

Thermodynamic Potentials: Gibbs Free Energy (G)

• G = H - TS.
• Its useful for processes at constant temperature and pressure.
• This determines whether a reaction will happen spontaneously.

Applications: Power Generation

• Applications include steam turbines and internal combustion engines.

Applications: Refrigeration and Air Conditioning

• Includes the use of heat pumps and refrigerators.

Applications: Chemical Reactions

• This is key for predicting equilibrium and reaction spontaneity.

Example Application: Heat Engine

• A heat engine converts thermal energy into mechanical work.
• Efficiency (η) is: η = W/QH = 1 - QC/QH, where W is work done, QH is heat absorbed, and QC is heat rejected.

Algorithmic Trading definition and advantages/disadvantages

• Algorithmic trading uses computer programs that automatically executes trading through pre-defined rules.
• Advantages include speed, accuracy, removes emotion, cost reduction and backtesting.
• Disadvantages include technical issues, need for market monitoring, model over fitting and possible market regime changes.

Common Algorithmic Trading Strategies: Trend Following

• Trend following assumes assets performing well continue to do so.
• Involves trend direction to trade in the direction of the trends.
• Moving averages and technical indicators help in identifying direction.

Common Algorithmic Trading Strategies: Mean Reversion

• This assumes asset prices eventually revert to their average level.
• You can identify assets deviated from their average price and trade in the opposite directions.
• Standard deviation and statistical measures identify mean reversion opportunities.

Common Algorithmic Trading Strategies: Statistical Arbitrage

• This involves exploiting small price discrepancies between related assets.
• Pairs trading identifies historical correlations and taking offsetting positions when conditions break down.

Common Algorithmic Trading Strategies: Index Fund Rebalancing

• Portfolio is rebalanced to maintain the target asset allocation
• Rules-based algorithms implement automatically. Used by index funds and other passive investment strategies.

Common Algorithmic Trading Strategies: Execution Algorithms

• Designed to execute large orders while minimizing market impacts and costs
• VWAP aims to execute orders at average asset prices along with a given period, Time Weighted Average Price (TWAP) executes evenly over a period.

Algorithmic Trading System Building: Data

• Historical and Real time price action is used.
• Also the usage fundamental, news and alternative types of data.

Algorithmic Trading System Building: Platform

• Coding languages from Python, Java and R
• Trading platform API is backtested using risk management tools.

Algorithmic Trading System Building: Strategy & Execution

• The trading strategy is defined, backtested and parameters are optimized.
• Execute live performance, monitoring and adjusts are also implemented.

Risk Management for Algorithmic Trading: Backtesting and Risk Controls

• Over fitting and failing transaction costs are limitations.
• Risk is controlled by position limits, stop-loss orders, and portfolio diversification which creates regular monitoring of performance.

Linear Algebra: Vector Spaces - Definitions

• An vector space is a set E and it must have two applications:
• Addition: $(u, v) \mapsto u + v$
• Multiplication: $(\lambda, u) \mapsto \lambda u$
• It must have an abelian group and external laws followed

Linear Algebra: Vector Spaces - Fundamental examples

• Example 1: $\mathbb{K}^n = { (x_1,..., x_n) \mid x_i \in \mathbb{K} }$
• Example 2: Matrix set $\mathbb{K}^{m \times n}$
• Example 3: function set $\mathcal{F}(X, \mathbb{K}) = { f: X \rightarrow \mathbb{K} }$

Linear Algebra: Vector Spaces - Subspaces

• A subset $F \subseteq E$ is a vector subspace if: $F \neq \emptyset$; $\forall u, v \in F, u + v \in F$ and $\forall \lambda \in \mathbb{K}, \forall u \in F, \lambda u \in F$
• $F$ is a subspace if: $0_E \in F$ and $\forall \lambda, \mu \in \mathbb{K}, \forall u, v \in F, \lambda u + \mu v \in F$

Heat Treatment Furnaces: Key Features

• Atmosphere Control to prevent oxidation.
• Temperature Uniformity for the chamber .
• Precise Temperature Control for the metal properties
• Automation (loading and unloading) increases efficiency and repeatability.

Batch Furnaces vs Continuous Furnaces

• Batch (Box, Pit, Bell, and Car-Bottom Furnaces)
• Continuous (Roller Hearth, Pusher, Walking Beam, and Rotary Hearth Furnaces)

Common Heat Treatment Processes

• Annealing softens the metal and improves ductility.
• Normalizing refines the grain structure.
• Hardening increases hardness.
• Tempering reduces brittleness of hardened steel.
• Case Hardening hardens the surface, leaving the core soft.

Different case hardening types

• Carburizing
• Nitriding
• Carbonitriding

Applications of furnace and material considerations

• Alloy Families (Steel, Stainless Steel, Aluminum etc).
• Used for Automotive, aerospace and tool industries.
• Important factors are efficiency and safety.

Order Execution systems: Course Overview, Objectives and Componenets

• Market machines and trading are understood, implement and automated.
• Lecture readings, quizzes and automated trading systems make analysis much easier. Technical analysis happens through event handling.
• Software in the cloud is helpful but basic finance, statistics and trading are not required.

Grading System

• Grading is achieved from projects, participation, reading
• Check canvas for updates.
• Ask questions during class

Honor Code & Developing the system

• Sources use original code
• Development is achieved by refining, live, paper trading and analysis and checking against market data.

Recursion

• Recursion involves something being defined that appears as a part of it's definition.
• recursive definitions involve an identification of well explained set of positive integers or numbers.

Recursive Algorithm

• Examples include towers of hanoi where there is decreasing amount of stack
• Procedure of toers includes a set of source, destination etc.

Information Asymmetry and selection

• When people have better information than others is information asymmetry.
• gathering third party information and group plans helps to make easier selection.

Moral Hazard and Principal Agent

• Incentive contracts and sharing information helps to increase moral standards.
• regulations can be a part of the principal agent where the principal can't monitor the agent

Bernoulli's principle equation, limitations, and examples

• Total energy remains constant when speeds are increased or decreased.
• Bernoulli's helps to explain airplane and some curveball movements that have density
• Incompressible, lack of viscosity and approximation for ideal fluids occurs.