arXiv subjects
Publications and source records attributed to B. K. Meister.
Caratheodory's axiom of adiabatic inaccessibility states that, in any neighborhood of a thermodynamic state, certain states remain unreachable via adiabatic processes. Non-arbitrage mirrors this topological restriction in finance. Preserving this constraint in resource-limited systems identifies the exponential family not as a modeling convenience but as the requisite geometric structure unifying both domains.
Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These findings break with the linearized liquidity models used in most decentralized exchanges. Second, a Constant Product Market Maker is viewed as a multi-phase Carnot engine, where one phase matches the exchange of tokens by a liquidity taker, and another the change of pool size by a liquidity provider. Third, stablecoin de-pegging is a form of catastrophe risk. By using growth optimization, default odds are linked to the cost of catastrophe bonds. De-pegging insurance can act as a counterweight and a key marketing tool when the law forbids the payment of interest on stablecoins.
In this brief comment we attempt to clarify the apparent discrepancy between the papers [1] and [2] on the quantum brachistochrone, namely whether it is possible to use a judicious mixture of Hermitian and non-Hermitian quantum mechanics to evade the standard lower limit on the time taken for evolution by a Hermitian Hamiltonian with given energy dispersion between two given states.
It is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of the system Hamiltonian during an isoenergetic expansion. It is shown that the existence of such a bath leads to equilibrium quantum states that maximise the von Neumann entropy. Quantum analogues of certain thermodynamic relations are obtained that allow one to define the temperature of the energy bath.
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.