Physics Applications in Finance, Trading & Investing

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Written By
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Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.

The Physics of Financial Markets is a relatively new discipline that approaches the financial world with the methods of physics – i.e., applying physics applications in finance, trading, and investing.

It’s a type of creative process that involves leveraging concepts and methodologies from physics to describe, understand, and predict the behaviors of financial markets.

It’s something that can help to “expand one’s horizons” and make connections between two seemingly dissimilar disciplines.

David Rubinstein’s book “How to Invest: Masters on the Craft” lists intellectual curiosity and skill in connecting the dots between seemingly unrelated pieces of information as one of the key skills of successful traders and investors.


Key Takeaways – Physics Applications in Finance, Trading & Investing

  • Physics of Financial Markets: Applying physics concepts to finance provides a unique approach to understanding market behaviors.
    • This interdisciplinary perspective can lead to improved trading and investment strategies by better uncovering underlying mechanics of systems or new mathematical approaches to model economic and financial phenomenon.
  • Econophysics: The fusion of physics and economics through econophysics enables the use of statistical and mathematical tools to explain economic phenomena.
    • This approach offers insights into, e.g., wealth distribution, stock/security price dynamics, and market downturns/crashes, drawing parallels with physical systems.
  • Quantum Finance: Integrating quantum mechanics into finance challenges traditional assumptions about rational decision-making.
    • Quantum finance provides tools to understand and capitalize on irrational market behaviors or find solutions to financial and economic problems where classic frameworks are lacking (e.g., options pricing).



Econophysics sits at the crossroads between economics and physics.

It seeks to apply statistical and mathematical tools, typically used in physics, to explain and predict economic phenomena.

  • This discipline has led to the development of models that describe how wealth is distributed among agents, the dynamics of stock/security prices, and other complex economic behaviors.
  • It has given us a new perspective on issues like market downturns, drawing parallels to phase transitions in physical systems.
  • Phase transitions in physical systems occur when matter changes from one state to another, like water to ice.
  • In financial markets, phase transitions analogize abrupt changes, such as market crashes, representing a sudden shift from one behavioral state to another due to underlying systemic conditions.


Social Physics

Social physics is about understanding human behavior and how it drives various societal phenomena.

  • Using data analytics and mathematical modeling, this discipline interprets the behavior of individuals and communities similarly to how particles in a system might behave.
  • This has been beneficial for finance, especially in understanding crowd behavior in trading environments and predicting market movements based on collective decisions.


Quantum Economics

Quantum economics delves into the application of quantum mechanics and quantum theories to economics.

  • The principle here is that traditional economic models often assume rational decisions.
  • However, in reality, human decisions often exhibit quantum-like behaviors where decisions aren’t always predictable.
  • This approach gives traders and investors new tools to understand and capitalize on irrational market behaviors.



Thermoeconomics, or thermodynamic economics, applies the laws of thermodynamics to economic processes.

  • It particularly focuses on the flow and conservation of energy within economic systems.
  • For investors, this can provide insights into how value is created, conserved, or lost in various market scenarios.

For example, the first law of thermodynamics is that energy is neither created nor destroyed.

So, if markets fall, is value really destroyed or did it simply go somewhere else? (Most wealth circulates rather than being destroyed.)

This thinking might lend one to believe that having balance in a portfolio is better if money and credit flows largely involve shifts among assets, asset classes, countries, and currencies.


Quantum Finance

Quantum finance is an interdisciplinary field that merges quantum physics theories and methods with economics to address challenges in finance.

This branch falls under econophysics.

Traditional finance, especially in the realm of instrument pricing like stock options, often faces problems that lack analytical solutions.

As a result, computational finance, which uses numerical methods and computer simulations, has become prominent.

Quantum Computing

However, many of these computational problems are complex and slow to solve on classical computers.

Quantum computing offers a potential solution.

Quantum computers have demonstrated superior performance in simulating quantum mechanics and other algorithms, making them a promising tool for computational finance.

Research in quantum option pricing often revolves around the quantization of the classical Black–Scholes–Merton equation, viewing it from the perspective of continuous equations like the Schrödinger equation.

The idea is that the traditional Black–Scholes–Merton equation might be a special case of the Schrödinger equation, suggesting that quantum models might offer more accurate pricing in certain scenarios.

  • The focus in quantum finance is mainly on option pricing, where classical models sometimes fail to capture the complexities of the market.
  • With quantum finance, more accurate pricing models can be developed, leading to better investment and hedging strategies.
  • Another example would be optimizing trading strategies by analyzing vast datasets faster, potentially offering a competitive edge in high-frequency trading environments.


Kinetic Exchange Models of Markets

Kinetic exchange models draw parallels between the exchange of money and the kinetic theory of gases.

  • The idea is that money, like particles in a gas, tends to distribute itself among agents in a predictable manner.
  • Understanding this can provide traders/investors insights into wealth distribution and how wealth flows within a market.


Brownian Model of Financial Markets

The Brownian model takes inspiration from Brownian motion, a random movement seen in particles suspended in a fluid.

  • In finance, this describes the seemingly random movement of stock prices over time.
  • Recognizing the underlying patterns in this randomness can aid in predicting stock price movements.


Ergodicity Economics

Ergodicity economics challenges conventional economic theories, particularly in how risks and rewards are assessed.

Ergodicity economics is a novel approach to economic theory that emphasizes the ergodicity question: whether the expected values of stochastic processes match their time averages.

This perspective offers alternative solutions to classical economic problems.

In decision theory, where expected-utility theory traditionally reigns, ergodicity economics presents different solutions.

At its core, ergodicity economics challenges the traditional use of expectation values, advocating for a more nuanced understanding that accounts for the ergodic or non-ergodic nature of the observables in question.

It emphasizes the importance of understanding the dynamics of decisions over time, contrasting with expected-utility theory, which focuses more on individual preferences.

  • The primary focus is on long-term outcomes rather than short-term fluctuations.
  • For traders, understanding market ergodicity can lead to better risk management and investment strategies.


Insights from Other Fields – Statistical Mechanics (Example)

Other disciplines can help us understand probability and its application to finance better.

Doing so aims to bridge the gap between the principles of other fields (e.g., statistical mechanics in physics) and their potential applications in the world of finance and trading.

What is Statistical Mechanics?

Statistical mechanics is a mathematical framework in physics that employs statistical methods and probability theory to understand the behavior of large assemblies of microscopic entities.

It doesn’t rely on any natural laws but rather explains the macroscopic behavior of nature based on the behavior of these microscopic assemblies.

This field has applications in physics, biology, chemistry, and neuroscience, aiming to clarify the properties of matter in aggregate.

The field has evolved to address both equilibrium and non-equilibrium situations, with various methods and approaches developed to tackle complex systems and phenomena.

Interdisciplinary Applications

Given that statistical mechanics has applications in biology, chemistry, and neuroscience, how can its principles be applied to financial markets, especially in understanding the aggregate behavior of traders and investors?

Macroscopic Behavior from Microscopic Entities

In finance and trading, can the aggregate behavior of markets be predicted by understanding the individual behaviors of traders, much like how statistical mechanics predicts macroscopic behavior from microscopic entities?

Equilibrium vs. Non-Equilibrium

Financial markets often oscillate between periods of equilibrium (stable prices) and non-equilibrium (volatile prices).

How can the principles of statistical mechanics, especially those related to non-equilibrium situations, be applied to understand and predict these market phases?


Applications of Statistical Mechanics

What are some potential applications?

Let’s take a look.

Applying Statistical Mechanics to Predict Market Movements

Looking at finance through the lens of statistical mechanics offers a unique perspective.

By analyzing the aggregate behavior of individual market entities, we can potentially forecast broader market trends, much like predicting macroscopic behaviors from microscopic interactions in physics.

For example, Boltzmann’s theories in physics can be applied to finance, suggesting that individual trader/investor/entity actions, when analyzed collectively, can predict overall market behavior.

If you look at who the buyers and sellers are in each market, how big they are, and what they’re motivated to do, you can build out distributions of what’s likely to happen.

Every trade, no matter how small, influences the market.

By examining these microscopic trades using statistical mechanics, we can gain a deeper understanding of macroscopic market trends and their driving forces.

Market Volatility: Insights from Non-Equilibrium Statistical Mechanics

Markets, like physical systems, can deviate from equilibrium (e.g., markets can get out of whack for liquidity reasons).

Non-equilibrium statistical mechanics provides insights into these deviations, helping us understand the underlying causes and potential effects of market volatility.

How Statistical Thermodynamics Can Explain Market Stability

Just as molecules reach a state of equilibrium in closed systems, financial markets tend to stabilize over time.

Statistical thermodynamics offers a framework to understand this stability, drawing parallels between molecular interactions and market dynamics.

Statistical Mechanics and Portfolio Diversification: Perspectives on Risk Management

By applying principles from statistical mechanics, investors can gain a fresh perspective on portfolio diversification, optimizing asset allocation to minimize risk while maximizing returns.

Parallels between Quantum Mechanics and Modern Portfolio Theory

Quantum mechanics, with its probabilistic nature, shares intriguing similarities with modern portfolio theory. Both fields deal with uncertainties, and drawing parallels between them can offer innovative investment strategies.

Financial Market Oscillations & Thermodynamic Systems

Financial markets oscillate between highs and lows, much like the fluctuations in thermodynamic systems.

By comparing the two, we might derive insights into market behaviors and potential future movements.

Entropy in Finance: Understanding Market Disorder through Statistical Mechanics

Entropy, a measure of disorder in physics, can be applied to financial markets to understand their unpredictability.

As we explained in a different article on decision theory, there are “known unknowns” (things we know we don’t know) and “unknown unknowns” (things we aren’t even aware that we don’t know).

Gibbs Ensemble and Asset Allocation: An Approach to Diversifying Investments

The Gibbs Ensemble, a concept from statistical mechanics, can be applied to asset allocation in finance.

By considering each asset/returns stream/investment as a part of an ensemble, investors can achieve a more diversified and balanced portfolio.

What’s an ensemble?

An ensemble in statistical mechanics refers to a collection of a large number of virtual copies of a system, each representing a possible microscopic state the system could be in.

These copies are considered simultaneously to provide a statistical overview of all possible configurations.

By studying the ensemble, one can derive macroscopic properties of the system, such as temperature or pressure, based on the probabilities of these microscopic states.

Essentially, it’s a tool to bridge the gap between microscopic behaviors and macroscopic observations.

Applications to finance and portfolio construction

Think of each investment as a unique song in a playlist. An ensemble in this context means considering all possible moods and tones each song (investment) can have.

When creating a balanced playlist (portfolio), you wouldn’t want all sad or all upbeat songs.

Similarly, in investing, you diversify by including a mix of assets, considering all their possible performances (their ensemble).

This ensures that if one song doesn’t fit the mood (an investment underperforms), others can still set the right tone, keeping your overall experience (portfolio) balanced and harmonious.


Other Forms of Statistics and Their Application to Finance and Trading

Note that while the analogy provides a conceptual framework, the direct application of statistical frameworks from one field to finance requires careful consideration and adaptation to the unique characteristics of financial markets.

With that said, let’s look at some examples:

Maxwell-Boltzmann Statistics

The Maxwell–Boltzmann distribution can be metaphorically applied to finance and trading.

Just as particles have different energy levels in a system, financial assets have different levels of risk and return.

The distribution can represent the probability of assets achieving certain returns or experiencing specific levels of volatility.

By understanding this distribution, investors can make informed decisions about asset allocation, diversifying their portfolio to achieve a desired risk-return profile.

In trading, understanding the distribution can help in predicting price movements and volatility, allowing traders to position themselves advantageously.

Essentially, the Maxwell–Boltzmann statistics provide a framework for understanding the behavior of a large number of entities (particles or assets) and their distribution across various states (energy levels or return levels).

Fermi-Dirac Statistics

The Fermi-Dirac statistics, rooted in quantum mechanics, primarily deals with the distribution of particles across energy states.

When applied to finance, trading, and investing, one could draw parallels between the behavior of particles and the behavior of assets, stocks, or commodities in a market.

Here’s a conceptual application:

Pauli Exclusion Principle & Asset Allocation

Just as no two fermions can occupy the same quantum state, in a diversified portfolio, no two assets should have the exact same risk and return profile (because they’re essentially the same thing).

This ensures a balance and reduces the risk of significant losses.

Distribution Over Energy States & Market Equilibrium

The F–D distribution describes how particles are spread over energy states.

Similarly, in a market, assets are distributed based on their perceived value and potential returns relative to their risk.

When the market is in equilibrium, assets are appropriately priced, reflecting their inherent risks and potential returns.

Thermodynamic Equilibrium & Market Stability

Just as fermions seek a state of thermodynamic equilibrium, financial markets tend toward stability.

External factors (akin to external energy in physics) can disturb this equilibrium, leading to market fluctuations.

Quantum Behavior & Market Anomalies

Quantum mechanics often defies classical intuition, leading to phenomena that can’t be explained by classical physics.

Similarly, markets sometimes behave in ways that don’t line up with classical financial theories or what normal distributions would predict (market returns tend to be fat-tailed), leading to anomalies that traders/investors seek to understand and capitalize on.

Bose–Einstein Statistics

Probability Distribution in Financial Models

Viewed purely as a probability distribution, the Bose–Einstein distribution can be applied to financial models to predict the behavior of assets or commodities that tend to occupy the same “state” or price level.

This can be useful in modeling assets that tend to cluster around certain price levels.

Term Weighting in Information Retrieval

Bose–Einstein statistics have been used for term weighting in information retrieval.

This can be applied to financial data analysis, where specific terms (e.g., greed, fear) or indicators (e.g., used to form the definition of a bubble) might have relationships with certain assets or market conditions.

This might have value to a financial historian trying to understand how economies and markets work, specifically under certain conditions.

Modeling Complex Systems

The evolution of many complex systems, including business networks, can be described using Bose statistics.

For instance, phenomena observed in competitive systems, such as the “first-mover-advantage” or “winner-takes-all,” can be understood as thermodynamically distinct phases of evolving networks.

This can provide insights into market dynamics, where early entrants might gain significant advantages or where certain assets or strategies dominate the market.

While the above points provide examples of a conceptual bridge between quantum statistics and finance, the application of quantum mechanics to finance is still a developing field.

Theoretical models that combine these two disciplines are being explored, but practical applications are still in their infancy.


FAQs – Applications of Physics in Finance, Trading & Investing

What is the Physics of Financial Markets?

The Physics of Financial Markets is a discipline that studies financial markets as physical systems.

It aims to understand the nature of financial processes and phenomena using the scientific method.

This approach avoids beliefs, unverifiable assumptions, and immeasurable notions that are sometimes present in economic disciplines.

The focus is on understanding the underlying processes and mechanics rather than just describing them.

How does Physics of Financial Markets differ from Mathematical Finance?

While both disciplines use mathematical models, the Physics of Financial Markets seeks to understand the nature of underlying processes, whereas Mathematical Finance is primarily concerned with descriptive mathematical modeling of financial instruments.

The former looks into the physical aspects and phenomena of financial markets, while the latter focuses on the mathematical representation of financial instruments.

What is Econophysics?

Econophysics is a multidisciplinary field that applies theories and methods from physics to study economic systems.

It particularly addresses issues like the theory of price formation, price dynamics, and market ergodicity.

By using tools from statistical mechanics and thermodynamics, econophysics aims to uncover patterns and behaviors in large economic systems.

What is Social Physics in the context of financial markets?

Social Physics is the study of how human behavior, particularly in large groups, can be understood using mathematical models.

In the context of financial markets, it looks at how collective phenomena, market self-action, and market instabilities arise from the interactions of individual market participants.

How does Quantum Economics differ from traditional economics?

Quantum Economics integrates principles from quantum physics into economic models.

It challenges traditional economic theories by introducing concepts like superposition and entanglement to explain market behaviors that are otherwise hard to rationalize using classical theories.

What is Thermoeconomics?

Thermoeconomics, also known as biophysical economics, is the study of economic systems using the principles of thermodynamics.

It looks at how energy flows and transformations impact economic processes, emphasizing the physical limits and constraints of economic systems.

How is Quantum Finance applied in trading and investing?

Quantum Finance applies quantum mechanics principles to financial modeling.

For instance, the concept of quantum superposition can be used to model complex financial instruments that exist in multiple states simultaneously.

This approach offers a more nuanced understanding of financial markets, especially in high-frequency trading scenarios.

What are Kinetic Exchange Models of Markets?

Kinetic Exchange Models are used to describe the exchange of wealth between agents in a market.

Drawing inspiration from the kinetic theory of gases in physics, these models look at how wealth is redistributed among market participants, leading to emergent market behaviors and wealth distributions.

What is the Brownian Model of Financial Markets?

The Brownian model of financial markets is based on Brownian motion, a random motion observed in particles suspended in a fluid.

In finance, it’s used to model the random movements of asset prices.

The model assumes that small, random fluctuations in price, when aggregated, lead to the overall movement of the market.

What is Ergodicity Economics?

Ergodicity Economics challenges traditional economic theories by questioning the assumption that time averages and ensemble averages are equivalent.

In simpler terms, it looks at how individual experiences over time can differ significantly from the average experience of a large group at a single moment.

This concept has implications for understanding risk and decision-making in financial markets.

Why is it essential to study the applications of physics in finance?

Studying the applications of physics in finance offers a fresh perspective on understanding complex market behaviors.

It’s more of a creative process designed to stretch one’s perspectives.

By borrowing concepts from physics, we can develop more accurate models, uncover hidden patterns, and gain deeper insights into the nature of financial processes.

This interdisciplinary approach holds the promise of more effective strategies in trading and investing.



The integration of physics and finance can yield a greater understanding of the mechanics of financial markets.

By looking at economic processes through the lens of physics, traders and investors gain a richer, deeper understanding of the forces at play, allowing for more informed and potentially more profitable decisions.