I would think a dollar today is necessarily at least as valuable than a dollar tomorrow, since a dollar today can either be a dollar tomorrow or a dollar today - i.e. it has optionality built in.
What is a dollar worth besides what it can purchase?
Put another way, if the number of dollars is constant in your account between today and tomorrow, but you can purchase less with it, you've lost wealth.
I understand but given the OPs comment, I would think it's always the case. Given the choice between a dollar today and a dollar tomorrow, you should always choose a dollar today since you can choose not to spend it. So it's strictly better than a dollar tomorrow.
The only time I see that it wouldn't be true is if there was risk in carrying it - taxes, negative interest rates, or theft. I could see for example a tonne of gold tomorrow being more valuable than a tonne of gold today since you'd have to deal with storage and security and such.
Everyone is right, there is a marginal bias so that the natural rate of interest is always positive but when storage costs and risk and fungibility/hedges/insurance are factored in the rate can be positive or negative. Like when the cost of oil was positive recently last year.
Put another way, if the number of dollars is constant in your account between today and tomorrow, but you can purchase less with it, you've lost wealth.