Thermodynamic entropy of a many body energy eigenstate

It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequal parts. It is argued that the entanglement entropy between these two subsystems is the thermodynamic entropy per degree of freedom for the smaller subsystem. This is done by tracing over the larger subsystem to obtain a density matrix, and calculating the diagonal and off-diagonal contributions to the entanglement entropy.Comment: 18 page

Information Causality as a Physical Principle

Quantum physics exhibits remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown state (no-cloning). Quantum correlations may be stronger than any classical ones, nevertheless information cannot be transmitted faster than light (no-signaling). However, all these features do not single out quantum physics. A broad class of theories exist which share such traits with quantum mechanics, while they allow even stronger than quantum correlations. Here, we introduce the principle of Information Causality. It states that information that Bob can gain about a previously completely unknown to him data set of Alice, by using all his local resources (which may be correlated with her resources) and a classical communication from her, is bounded by the information volume of the communication. In other words, if Alice communicates m bits to Bob, the total information access that Bob gains to her data is not greater than m. For m=0, Information Causality reduces to the standard no-signaling principle. We show that this new principle is respected both in classical and quantum physics, whereas it is violated by all the no-signaling correlations which are stronger that the strongest quantum correlations. Maximally strong no-signalling correlations would allow Bob access to any m bit subset of the whole data set held by Alice. If only one bit is sent by Alice (m=1), this is tantamount to Bob being able to access the value of any single bit of Alice's data (but of course not all of them). We suggest that Information Causality, a generalization of no-signaling, might be one of the foundational properties of Nature.Comment: This version of the paper is as close to the published one as legally possibl