Entropy and Accounting

35 Pages Posted: 13 May 2019

See all articles by John C. Fellingham

John C. Fellingham

Ohio State University (OSU) - Department of Accounting & Management Information Systems

Haijin Lin

University of Houston

Douglas Schroeder

Ohio State University (OSU) - Department of Accounting & Management Information Systems

Date Written: April 12, 2019

Abstract

In this paper we establish an equivalence between accounting numbers and information. The information numbers are denominated in entropy which is a measure of uncertainty and is a function of probabilities only. Mutual information is defined as the reduction of entropy when an information source X is available. We state that the log of one plus the accounting rate equals to the sum of the risk free rate and mutual information. Three conditions are sufficient: (i) long run decision frame; (ii) arbitrage free prices; and (iii) accounting valuation approximating discounted cash flows while the discount rate is the sum of risk free rate and mutual information.

We derive two versions of the equivalence; they differ only in the measure of mutual information. One version is for when states of the world are observable and mutual information is the reduction of classical or Shannon entropy. If all possible states of the world are observable (and contractible), then all transactions can be consummated in the marketplace. Hence, firms, and the accounting for firms, might not arise. We extend the results by modeling state unobservability using quantum measurement techniques. The equivalence relation remains the same with quantum measurement probabilities substituted for classical probabilities and mutual information is the reduction of quantum entropy. The classical state observable case is seen to be a special case of the quantum equivalence.

Keywords: information, accounting rate of return, Shannon entropy, quantum entropy, mutual information

JEL Classification: C61, D81

Suggested Citation

Fellingham, John C. and Lin, Haijin and Schroeder, Douglas, Entropy and Accounting (April 12, 2019). Available at SSRN: https://ssrn.com/abstract=3371246 or http://dx.doi.org/10.2139/ssrn.3371246

John C. Fellingham

Ohio State University (OSU) - Department of Accounting & Management Information Systems ( email )

2100 Neil Avenue
Columbus, OH 43210
United States
614-292-2488 (Phone)
614-292-2118 (Fax)

Haijin Lin (Contact Author)

University of Houston ( email )

390F Melcher Hall
Bauer College of Business
Houston, TX 77204-6021
United States
7137437771 (Phone)

Douglas Schroeder

Ohio State University (OSU) - Department of Accounting & Management Information Systems ( email )

2100 Neil Avenue
Columbus, OH 43210
United States
614-292-6427 (Phone)

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