The Physical Meaning of Money

Is there a physical meaning to money? The book Entropy God’s dice game ends with a statement that freedom is entropy, equal opportunity is the second law, and the microstates in which we exist is our destiny, that was determined in God’s dice game. The reasoning behind this, somewhat bombastic, statement is that the higher the freedom, the higher is the number of the microstates available for us, and therefore the higher the entropy. The entropy has a maximum value when there are no constraints and each state (and therefore each microstate) has equal probability. It is also argued in the book that in networks the number of links of a node represents its wealth. For example, in our society, Bill Gates is linked, that is to say, has access to many people, due to his wealth. In the paper “Money, Information and Heat in Social Networks Dynamics” that was recently published at “Mathematical Finance Letters”, this argument is further investigated. In this paper a network is defined as a microcanonical ensemble of states and links. The states are the possible pairs of the nodes in the nets, and the links are communication bits exchanged between the nodes. This net is an analogue to people trading with money. This approach is consistent with the intuition of the book that wealth is entropy (information), and therefore money is entropy, which can be interpreted as a freedom to choose from many options. Therefore, the physical meaning of money is entropy. In this case, money transfer is simulated by bits transfer which is heat (energy transfered). With analogy to bosons gas, we define for these networks’ model: entropy, volume, pressure and temperature. We show that these definitions are consistent with Carnot efficiency (the second law) and ideal gas law. Therefore, if we have two large networks: hot and cold having temperatures TH and TC, and we remove Q bits (money) from the hot network to the cold network, we can save W profit bits.  The profit will be calculated from W< Q (1-TH/TC), namely, Carnot formula. In addition it is shown that when two of these networks are merged, the entropy increases. This explains the tendency of economic and social networks to merge. The derived temperature of the net in model is the average number of links available per state.