Quantum Entropy and Accounting

Richard Tabor

Nilanjana Datta

John C. Fellingham, Haijin H. Lin, Doug Schroeder

This monograph analyzes accounting using information theory developed by Claude Shannon and others. A three-way framing equivalence is derived (i) when states are observable; and (ii) when states are not observable and only a signal is observable where the signal reports the state with error. The equivalence establishes equality of accounting numbers, firm rate of return, and the amount of information available to the firm where Shannon’s entropy is the information metric. The major assumptions used in deriving the state observable equivalences are constant relative risk aversion preferences, arbitrage free prices, and geometric mean accounting valuation. State unobservability is modeled using the quantum axioms, and, hence, quantum probabilities; the state is unobservable in the same way quantum objects are unobservable. The state observable equivalence is seen to be a special case of the state unobservable equivalence. Quantum probabilities allow analyzing the effects of entanglement, a phenomenon not occurring when classical probabilities are used. Entanglement is seen to be a powerful economic force, and caused by instantaneous communication of information. We speculate double entry accounting can be a mechanism for creating entanglement effects as (i) double entry accounting conveys information relevant to the expected return maximization and entropy reduction; and (ii) it does so instantaneously as the same number is simultaneously available in two places (due to double entry)..

Stefano Marcantoni, S. Alipour, F. Benatti +2 more

In the weak-coupling limit approach to open quantum systems, the presence of the bath is eliminated and accounted for by a master equation that introduces dissipative contributions to the system reduced dynamics: within this framework, there are no bath entropy contributions to the entropy balance. We show that, as a consequence, the entropy production fails to be positive for a class of physically legitimate, that is completely positive and trace preserving, non-Markovian dynamical maps. Moreover, in absence of the semigroup property, if the reduced dynamics has a thermal asymptotic state, this need not be stationary. Then even the integrated entropy production becomes negative. These observations imply that, when the conditions leading to reduced dynamics of semigroup type are relaxed, a consistent formulation of the second law of thermodynamics requires that the environment contribution to the entropy balance be explicitly taken into account.

Masanori Ohya, Dėnes Petz