Time Crystals, Non-Equilibrium, and Financial Risk Management

It is now widely acknowledged that, by nature of their design, the models developed by neoclassical economists to simulate the economy, from models of financial risk used by banks to the macroeconomic models used by policymakers, failed to predict or even accurately explain the events of the 2007-2008 Global Financial Crisis. In fact, they also contributed to the crisis by creating a false sense of security, namely one related to so-called optimal market equilibrium. 

Optimal market equilibrium is the wrong objective

But, we have been told a lie: the state of optimal market equilibrium is an entirely imaginary state, and so no such invisible hand exists. Such a hypothetical state would reflect complete satisfaction and happiness on the part of every individual on the market. It would render any further entrepreneurial action superfluous, as action is prompted by the desire to change one’s current situation. In reality, individual value preferences continuously change. New, more efficient utilization of factors of production is continually being discovered. Entrepreneurial innovation continually identifies new future demands.

An essential foundation in risk management, and in particular concerning market risk management is the general equilibrium theory. Indeed, the Capital Asset Pricing Model (CAPM), which was developed in the mid-1960's, utilizes several hypotheses about investor and markets behavior to give a set of equilibrium conditions that allow us to forecast the return of an asset for its level of systematic (or nondiversifiable) risk.

And, the market equilibrium in the CAPM is an important construct to understand the changes that occur on the market. Indeed, the process of price formation and the actions prompted by it are deemed to tend to move the market progressively closer toward the condition of market equilibrium. As value preferences, alter and discovery of more efficient ways of production occur, so does the potential state of market equilibrium. Actors on the market perform actions that again move the market data closer to this equilibrium which, however, remains in constant flux.

However, believing far too credulously in optimal market equilibrium and an invisible hand, the Federal Reserve Bank failed to predict the subprime crisis. The principal models it used posited that markets are always in instantaneous balance, so how could a disaster occur? But after the global financial crisis exploded, the Federal Reserve Bank dropped its high-tech invisible-hand economic models and responded with full force to provide support to the economy. The powerful invisible-hand metaphor refused to let go. It assured German Chancellor Angela Merkel, even if she was raised as a child in East Germany under Marxism-Communism that slashing fiscal budgets and deregulating labor markets would bring the euro crisis to an end. Based on thinking dimmed by some invisible-hand fancy, European political authorities have again and again been a day too late and a euro short in responding to market gales. Subsequently, they made the euro crisis far worse than it had to be.

Financial risk management could learn a lot from time crystals

For that reason, the financial markets industry could learn a lot from the quantum world, and in particular from the latest developments as they relate to time crystals. This does not mean that financial markets should directly mimic quantum physics, or adopt the formalism of quantum mechanics. Instead, financial markets should be viewed as a quantum system on its terms, with its versions of duality, measurement, uncertainty, entanglement, and so on.

The world around us is formed from non-equilibrium conditions, such as the structure of the universe, turbulent flow, life itself, and social activities. Research on such processes and systems may assist in identifying the rule of randomness and acknowledge the importance of the role of correlated degrees of freedom in the organization and transport of energy and matter. Such quest for universality is motivated by a hope of identifying emergent principles governing non-equilibrium systems.

Different regions of a system are so unlike one another that they cannot reach equilibrium. It turns out that these highly disordered, non-equilibrium systems can both sustain interesting quantum dynamics over long time periods and lead to totally new types of quantum matter. In these systems, the push toward equilibrium driven by interactions among particles is curbed by disorder, slowing down the scrambling of quantum information. 

In everyday life, if you put milk in your coffee, it mixes, and you can measure an average quantity to show that the coffee is more creamy. But you can’t measure what happens with every particle. The scrambling of information that takes place as a quantum system moves toward equilibrium is effectively irreversible. The initial data still exists, but when you let the system evolve, all the correlations among particles that account for this initial information are mixed over the entire sample in a very complicated way that you can never retrieve. While most systems we know behave in this way, recent breakthroughs in atomic physics have allowed us to produce systems that do not equilibrate even over in nite time periods. Some networks scramble information quickly, and some scramble it slowly.

However, while equilibrium or stability never exists, we humans have always tried to reach that kind of ideal balance. But, we should review our approach and change it. Indeed, for the last half-century, we have been exploring equilibrium matter. Now, with the discovery of time crystals the doors are starting to open toward the exploration of a whole new landscape of non-equilibrium matter. 

Indeed, Harvard scholars discovered in 2012 a new state of matter, dubbed a time crystal, a find that brings about new avenues of research and potentially paves the way for the development of quantum sensors and quantum computers. Companies such as NEC Corp, Mitsubishi, Nokia Bell Labs, Alphabet Inc.’s Google, Microsoft Corp., Rigetti, Airbus, Lockheed Martin, D-Wave, Raytheon, Amgen, Biogen, and IBM Corp. are in an advanced stage for the development of quantum computers, which they suggest will have future applications in cybersecurity and artificial intelligence.

Source: Chemistry Libre Texts

Time crystals: the fifth (sixth0 matter and fourth dimension

As a reminder, in physics, a condition of matter is one of the singular forms in which matter can exist. Four states of matter are identifiable in everyday life: solid, liquid, gas, and plasma (i.e., and a fifth one: Bose-Einstein condensates) - the main difference in the structures of each state is in the densities of the particles. Traditionally speaking, crystals - such as sugar, salt, or even diamonds - are merely periodic arrangements of atoms in a three-dimensional lattice. While time crystals, on the other hand, take that notion of periodically-arranged particles and add a fourth dimension, indicating that - under certain conditions - the atoms that some materials can portray periodic structure across time.

Source: Princeton University

In other words, a time crystal or space-time crystal is a structure that is repetitive in time, as well as in space. Ordinary three-dimensional crystals have a repeating pattern in space but do not change as time passes. Time crystals repeat themselves in time as well, leading the crystal to modify itself from moment to moment. A time crystal never reaches (thermal) equilibrium, and that is a concept that could prove crucial in also understanding dynamic financial and economic systems.

Time crystals are not only a new phase; they represent one of the first examples of an intrinsically out-of-equilibrium phase of matter. Indeed, the crystal-like behavior could theoretically exist in a system that receives periodic nudges and never settles down to a motionless equilibrium.

And just like for quantum theory, the financial markets industry could learn a lot from the world of out-of-equilibrium quantum systems, such as time crystals. This does not mean that financial markets should directly mimic the environment into which time crystals evolve, or adopt the formalism of time crystals. Instead, financial markets should be viewed as a time crystal system on its terms, with its versions of duality, measurement, uncertainty, entanglement, and so on. 

Finding stability in out-of-equilibrium

Again, in neoclassical economics, ‘market failures’ such as economic inequality, financial instability, and environmental degradation are treated as aberrations or externalities. Time crystals give us a tantalizing window into the behavior of such out-of-equilibrium systems because time crystals can’t settle down to a motionless equilibrium.

And this is where financial markets (as well as social systems such as politics and economics) could find a rationale: instead of always seeking an equilibrium, it would be better to accept that the environment into which financial markets evolve is motionless - similar to time crystals as they can never settle down.

In other words, instead of driving something into equilibrium to increase its stability, one should be driving something out of equilibrium to improve its stability. A good illustration of this is the famous trick of making an inverted brush stand up on one of your fingertips or the palm of your hand. If you hold your hand still, the brush is unstable and will tilt over quickly. But if you drive the brush out of balance by moving your hand around periodically, you can make the brush very stable, so it remains upright and steady indefinitely.

A financial system (but also any other social system) is made of a myriad of (in)direct actors whose actions are entangled and very sensitive to each of the environments into which they operate. You can find a similar metaphor with particles in a quantum state that are very sensitive to their environment. With the slightest disturbance, they can lose their predictable and measurable properties. We need to accept that the financial (but also economic and political) world is complicated, motionless, and sensitive to tiny changes (similar to the butterfly effect).

Resiliency is the answer

Therefore instead of pouring massive resources into trying to seek an imaginary equilibrium and stability, or attempting to predict the future (i.e., predictive analytics), it is better to design business models that are resilient to changes and agile. Statisticians, risk managers, financial analysts or economists, if history is any guide, have a notoriously bad track record in terms of predictions: not only did the lion share of them fail to forecast the Global Financial Crisis and the Great Recession, they also failed to predict most of the previous financial crises and economic recessions or even to recognize them until after they had erupted. 

Why? Just because, it is very difficult to understand an organism as complex as the world of finance, the economy or a political environment and to forecast their evolutions and cycles. These social systems (finance, economics, politics) are indeed dynamic, complex systems, comprised of a multitude of elements that continuously evolve and interact in various ways, meaning that some of its aspects are likely to elude any interpretation that may be made at any given point in time. The so-called pundits’ answer to this difficulty has largely consisted in evacuating whole aspects of the complex social system from their view and in reducing their field of inquiry to a limitative set of relatively basic components that they contend can be ‘scientifically’ described and measured. 

Resilient business models, economies, and societies can absorb shocks and stresses, even those as severe as the recent financial crisis. Indeed, most business and policy processes follow a linear logic: they aim to optimize the desired result while seeking to cut down redundancies in the name of efficiency gains. This method, geared towards reaching and maintaining the equilibrium, undermines the capacity to absorb disturbance and reorganize while changing within a system – be it social, economic or ecological. Subsequently, the system becomes brittle; vulnerable to unforeseen perturbations.

Preventing these unintended consequences of these business and policy interventions requires a thorough understanding of the dynamics and interconnectivity of the financial markets, the economy, society, and environment. Again, in neoclassical economics, ‘market failures’ such as financial or economic instability, is treated as aberrations. And, time crystals give us a tantalizing window into the behavior of such out-of-equilibrium systems, because time crystals, similar to financial/ economic/ political systems, cannot settle down to a motionless equilibrium.